I've been able to group a bunch with no AE missions... the key is not to be in AP and have your looking for anything indicator turned on.
Yes, people group outside of AE all the time.
If you're having trouble, you can do a few things:
1) Set your LFT comment to "No AE missions"
2) Form your own teams
3) Looking into Freedom's forum, and advertise for groups there (either by forming your own, or looking to join a group that is non AE-focused).
4) Get out of Atlas Park and look for teams elsewhere.
Let me never fall into the vulgar mistake of dreaming that I am persecuted whenever I am contradicted.
~Ralph Waldo Emerson
"I was just the one with the most unsolicited sombrero." - Traegus
The "Ways you see most frequently" to find groups work really badly, but are conspicuous. Broadcasting, for instance, is not very effective.
Setting your search tag to "looking for anything" helps sometimes.
Setting your search field to something useful ("rad/sonic. I make damage!", or "Throatcutter for justice", or whatever) helps sometimes.
Joining a global channel- I don't know the ones on Freedom very well, because a lot of them are full- helps a lot. You can say "Anyone want a level 32 broadsword scrapper" or whatever you are.
Someone's going to say "Form your own teams" and it might as well be me. If you do so, let people know what kind of team. "Small L32 team to do invincible Freakshow missions, interested?" is a good invite. "Join my team?", not quite as good. Blind invite... often blind rejected.
EDITED BECAUSE I LEFT OUT THE IMPORTANT ONE:
If you find a good player on a bad team [and you will get a lot of bad teams, even if you build them yourself] right click and "Friend" them. "Global friend" if you think of it, but don't take it personally if they turn you down. Gfriends can stalk you. It could happen.
Eventually you will have a network of people and you can ask "Whatcha doing?" and get an answer, maybe even a team. That doesn't help you NOW but it will help you SOON.
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I'll add another method. Join, form, or coalition with an active supergroup.
Badge, Task Force, LFT or Forums channels can be very productive. Join them if you can.
AE missions can be boring repetitive farm-fests, but they also can be entertaining, challenging, and well-written. There is good content in the MA.
Forming your own teams is the best guarantee-er of running the content you want. Be polite, pay attention to search comments, and give a lot of information in your opening tell.
EDIT: Be polite, pay attention to search comments and flag settings, and give a lot of information in your opening tell. You could use macros, but I see it as an opportunity to practice speed typing 
www.paragonwiki.com is a great source of information for this game.
New or returning to the game? Want advice from experienced players who want to help YOU?
The Mentor Project: Part of the New Player Council.
I've been running 8-man teams every weekend, even at the height of AE farming.
...I forgot what experience means.
[ QUOTE ]
Yes, people group outside of AE all the time.
If you're having trouble, you can do a few things:
1) Set your LFT comment to "No AE missions"
2) Form your own teams
3) Looking into Freedom's forum, and advertise for groups there (either by forming your own, or looking to join a group that is non AE-focused).
4) Get out of Atlas Park and look for teams elsewhere.
[/ QUOTE ]
5) Get off of Freedom. It seems to be the server that hasn't got the memo that farms were nerfed.
Do what the others said about getting out of Atlas and setting your teaming flags.
We have a designated weeknight for doing Taxibot-created AE stories for fun. Other times, we have no trouble recruiting for (say) regular contact missions, task forces, etc.
-Johnny
The only times I've grouped so far is to teach a new player some mechanic of the game by malefactor. Otherwise I'm solo.
Now if only 'I' could get party credit for 'me' and 'myself' as well, I'd be even happier.
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I group almost exclusively NOT in AE.
(Sometimes, I wish there could be a Dev thumbs up button for quality posts, because you pretty much nailed it.) -- Ghost Falcon
Teaming in AE doesn't give purple recipes. Screw AE.
I grouped last night with some friends doing normal radio missions, so yes people still do group outside of AE 
I had an epic group last night, we ran every mission in the hollows then we went and killed the kraken as a grand finale.
It was more fun than a AE group could ever be. We had more variety in the missions rather than just your standard AE mission that seems to be get into a group of 8, auto SK to 50 then kill group after group of lieutenants and bosses then rinse and repeat on the same mission.
Use the grouping flags. The only ones who don't are the AE newbies. Also try messaging in broadcast for a non-AE team.
I've been lucky in that I'm part of a large global channel group (don't ask for an invite, we're pretty exclusive) and we almost always have a few teams running.
We mostly do radio and AE story arcs, with the odd high end mission or RWZ team. For fun, we often have "baby" hero or villain groups on fresh/lowbie characters.
Ok...been back for about a week now and it seems that all anyone wants to do is AE missions?
Is this true or am I just having no luck. Im normally on freedom server