Listen to some of the comments when you rescue people. "You capes aren't all that bad" or "Maybe I was wrong about heroes?" or things to that effect. Trying to think up of some other cases or sources, but it's a little not-forthcoming at the moment.
I myself would say that Mutants would be accepted in todays society, but like racism / sexism unfortunatly pockets of people will still protest, i'd put Mutants in the same category, but with the vast majority of the public viewing Mutants as one of their own not as 'freaks' but thats just my look on it, and from what ive seen during Roleplay. 
From what I have heard from other people I think there's one case of someone suffering persecution because of their mutant origin.
My main character Coile is a mutant and has never had any trouble from other peopl because of his mutant nature, but his background also put him in very little contact with others for a few years before coming to Paragon City, so I have not had to make any real calls about the subject so far.
As a personal feeling I'd say that in general mutants are just supers. Not worse or better. If I wanted to give a character hard time just for being mutant I'd opt for a closed group and not define the detriment to be universal.
Lunk for one has a major gripe against mutant supremacists (same as he would other racial or cultural supremacists) and has ended up in heated arguments with "mutates" because of this (mostly due to those mistaking his opinions for being anti mutant)
in general, mutants are accepted as much as anyone else with similar levels power or freaky-looking-ness.
From what I've seen and read; and i've been here since EU beta, there's no anti-mutant prejudice in the game lore. There IS, however, some anti-cape prejudice; be they mutant, science, tech or whatever.
There's also a certain amount of xenophobia towards aliens too.
@FloatingFatMan
Do not go gentle into that good night.
Rage, rage against the dying of the light.
Most prejudice is based on the difference between people, and nowhere is this difference more obvious than between the the normal citizens of Paragon City and the Heroes.
Not only do the Heroes of Paragon City have these powers which the normal folks can only dream about, but they also dress themselves differently!
I think there would be a general level of prejudice and mistrust purely based on these differences, regardless of what origin you were.
Just because you show yourself to do good deeds, that doesn't mean that people will trust you.
Formerly @Crimson Archer, now @CA
The Militia - Protecting Paragon City through roleplaying since June 2006!
In my teens I was a big fan of the Marvel Mutant titles, that said I think the kind of prejudice seen there is not prevalent in the Paragon universe.
As Crimson Archer said I think most prejudice is from normals towards super powered beings in general, I would venture to guess that Natural human heroes are far more accepted.
Generally speaking one of the things I really like about this setting is that it seems to have properly integrated the reality that there are super powered beings. In the USA heroes are registered and accountable for their actions from 1937 with the Citizen Crime Fighting Act.
I think this suggests that all meta humans are a lot more integrated in society then in most comic book settings, that said a lot of suspicion and distrust can still foster in some groups.
Shadowplay - Scrapper DM/DA SL 50
Doctor Storm- Brute SS/Elec SL 50
"speed boosts someone in the face" - Cognito
Due to her background, Sabrina San (Dragonfly) who was trained from childhood as a ninja generally believes in human supremacy. After a clan war in her home town, she migrated to Paragon City and has since been at odds with androids like Nene (Number Nine), mutants like fellow teammate Saffron McKenzie (the Amber Banshee) and aliens such as Vanyanarore the Elendevian (Dark Silver). Over the years though, she has made some progress, however little, to accept the fact that here in America, she is surrounded by freaks and there is nothing she can do about it. Either blend in (and watch reruns of Sweet Valley High) or go back home. Come to thing of it, its no wonder she sometimes comes across as anti-hero (or maybe thats just due to her attitude problems).
Anyway, I would imagine its a similar relationship between the civilians of our City and the super-powered. Some folks would feel threatened because they don't really know or understand supers. Some would envy them, and envy leads to hatred. Some would blame them for all their problems. And other civilians, like poor Sabrina, really do support human supremacy and are probably against mutants; the so-called evolution of mankind.
But to wrap up, as has already been said, some civilians in Paragon and the Rogue Isles are indeed anti-mutant, but more so, they are anti-super. Having said that, you'd be hard-pressed to find any of these people out and about. The majority are fans and supporters of brightly coloured spandex.
I choose a different apporach, a kinda reserve racism to mutants, if you will. UltraNova was a mutant from an early child hood, and when he first moved to paragon he wanted to be a journalist, but because he was a mutant everyone pushed him into being a hero. They looked at his profile and said "Oh your a mutant I see... wouldn't you be happier as a hero?"
There is one possible group that might be Anti-mutant in the game...but they're never actually met, you only ever see their posters.
Humanity First.
You never encounter Humanity first in the game (Brit has really made his own (in a good way) and helped create an RP villain group not in the game normally). With slogans like 'Earth for Humans' a dedicated anti-super person could read that as earth for normal humans and that all those who weren't normal (which would include all super-powered heroes, villains and groups like Trolls etc.) should be 'removed'.
That's about the only group I can think of that would be anti-mutant but then they would more than likely just be anti-superpowered so I don't really think there's any specific anti-mutant feeling in the game, just as the many other posters have said, anti-cape.
Badge Earned: Wing Clipper
A real showstopper!
Those Humanity First posters are put up by the Vanguard. It's not their name, it's their slogan. 
@FloatingFatMan
Do not go gentle into that good night.
Rage, rage against the dying of the light.
Actually as Mechano said Humanity First are a villain group I created (inspired by those Vanguard posters), who are anti-pretty much anything not baseline human.(Partisan their leader is an equal opportunities bigot )
While Humanity First dont just inflict their brand of terror, and racism against mutants, many bear the brunt of Humanity First's activity. After all many mutants would try to continue living normal lives, and not go into heroing, or villainy making them easier targets for Humanity First.
Also the name mutant is easily used as a negative label to describe anyone different. Just labelling something as a mutant seems to add an extra level of threat ie. "the mutant criminal leader Frostfire yadda, yadda, yadda!"
Frostfire is not just a mere criminal hes a mutant criminal.
Partisan being adept at psychological warfare often preys on the fear of the normal populace, and will readily use such labels as mutant to stir up trouble.
I think in CoX I think people's opinions on metas, and mutants in particular would be heavily influenced by events in the media. If dangerous mutant criminal pops up a lot then people will start thinking all mutants are dangerous. etc.
As for Humanity First in game I tend to only use them for story pieces such as Riot in the Row during the Tempest Virus scare, or in Big Game's Burning Bridges. Problem is when I tried to run it as a proper SG it was very difficult to find people willing to stay within the theme.
Anyway il leave you with an early Humanity First propaganda flier, as well as the thought that although mutants may not necessarily be universally hated they are perhaps an easy group to be targetted for bad press.
http://i145.photobucket.com/albums/r.../vitruvian.jpg
He referred to the "Humanity First" posters actually physically in the game. Those are put up by the Vanguard.
@FloatingFatMan
Do not go gentle into that good night.
Rage, rage against the dying of the light.
ah nuts...shows how much attention i paid to them (I heard of Brit's Humanity First BEFORE playing CoH and seeing the posters...just assumed Brit had seen the name on the posters and ran with it, never noticed the Vanguard part).
Doh! Sorry on my part there.
damn I look foolish.
Saying that...knowing what I now know about those posters...makes Vanguard seem alittle darker and a lot less cosy than I had initially taken them for (Hey I only dinged 35 in the wee hours of this morning on my main and only just got into RWZ)...If we weren't helping them with the Rikti...they'd be trying to pummel our faces in no doubt...Hero and Villain.
Badge Earned: Wing Clipper
A real showstopper!
Imagine how my Peacebringer feels about them! Bunch of xenophobic bigots that they are!
@FloatingFatMan
Do not go gentle into that good night.
Rage, rage against the dying of the light.
and they're backed by the UN...damn...they're almost as bad as Longbow.
Come on Longbow are TOO good...creepy kind of good...you know when someones acting really nice to cover up for the fact they're actually quite creepy and psychotic...atleast Arachnos are pretty much upfront about what they're doing.
Yeah...starting to see Vanguard in a whole new light...plus they're making me rescue LONGBOW...come on I butchered over a 1000 of them (got the villain badge) it's not like I really want to be saving their hides...and I imagine they'd rather a hero did it than a villain whose cause more casualties than a small war on them...
Badge Earned: Wing Clipper
A real showstopper!
Earth for humans is a reasonable sentiment considering, plus the Vanguard cooperates with Peacebringers and Warshades. Hard military and practical is what I get most from the Vanguard.
Shadowplay - Scrapper DM/DA SL 50
Doctor Storm- Brute SS/Elec SL 50
"speed boosts someone in the face" - Cognito
That's NOW, yes... Before i10 though, all we had to go on was the posters; and you can't deny they're xenophobic in nature.
@FloatingFatMan
Do not go gentle into that good night.
Rage, rage against the dying of the light.
The posters have a strong propaganda flavour, they are made to instil fear and vigilance towards the Rikti and possibly other extraterrestrial threats. This means they might propagate xenophobia but it says nothing about the organisation itself.
Anyway, part of my point was that as ugly as discrimination is, it makes perfect sense that it would exist culturally to some extent considering the destruction the first Rikti war brought.
Peacebringers/Warshades are a bit of a special case within itself, the fact that they are part human and might still have brothers, sisters, spouses and friends from the time they where still fully human makes their case interesting.
PS: Just pondering and babbling I understand your point FFM.
Shadowplay - Scrapper DM/DA SL 50
Doctor Storm- Brute SS/Elec SL 50
"speed boosts someone in the face" - Cognito
A few days ago, I had an IC discussion at Pocket D about mutants being "misstrusted" by the common person. The guy I was talking to (don't remember the name) thought that it was strange that people misstrust mutants, but are all for other sorts of superpowered beings, like those who's had a lab accident or just decide to train themselves to human perfection, etc. While I actually agree that this is strange, I see one problem with the whole discussion: I don't think mutants in the CoH-universe are seen as any different than other types of superpowered beings. Consider the description that the official homepage give of the mutant origin:
"These powers set the mutant apart from the rest of mankind; they are capable of far more than any normal human being. Mutants are sometimes feared for their strange talents, but are more often admired by the public at large."
Now, I do think that the whole "why are mutants feared but not other spandex-folks" is a good question... In the Marvel universe. But that's a whole other discussion, for a whole other forum. In CoH, I think the thing to be discussed would be people's opinion on superpowered people in general. And from what I understand, that opinion seems to be pretty positive, at least compared to some other superhero universes. To me it seems far more likely for the Paragon Times to write an article called "Heroes Halt Havoc" than one called, say, "Positron: Hero or Menace?"
I'm not entirely sure wheter this positive opinion is the right one to have. After all, lots of the crime and general hardship in Paragon is done by superpowered individuals. But maybe people are just glad that whenever some masked punk tries to steal your purse, chances are high that a caped crusader will stop by and punch them in the face.
What do you think? What is the public opinion about superheroes in Paragon, and in the CoH-world at large?