I'd recommend looking for channels as opposed to SGs. A lot of players now have solo 1-person SGs and interact primarily through channels.
I don't know of any RP-oriented SG, so I can't help you in that regard, but I found that SG activity for the most part isn't very active, while teaming opportunities, including opportunities to RP, abound in channels.
We do both We even have designated weeks for it.
Fair warning, though, the banter can get..... banter-y, and the OOC discussions on the designated channel can be a little rough for new people to handle. We will and can debate anything and everything in an open forum, so if you're easily offended, this is probably not the place for you to linger in.
Cynics of the world, unite!
Taking Care of the Multiverse
The Jadewire is RP and we love doing missions and TFs. Yeah, sometimes we do base RP, but we also have fun leveling and doing builds. http://thejadewire.mmoguildsites.com/
The United Sentinels of America are a 'both' SG as well. Currently, we have 1 every other week Monday scheduled or what we call open RP, which sometimes means socializing in the base, sometimes doing RP missions, sometimesa bit of both.
Activity in-between the every other week thing is at the moment a bit low. Always people in the OOC channel though, with many ready and able to rp mission on any number of characters.
*hangs head in shame*
The lot of us are poster children for altaholics anonymous...
Feel free to give me a shout @Shaw Lwhon.
Twipper
The Supreme Society actively RPs during missions, but we're a VG. 
well a VG you say i might have to look you guys up
I know there's a thread for SGs to post their info on and I could look through that... however I have never found the information I've been looking for in that method. So here goes.
Where can i find an ActiveRP SG as opposed to an Active RPSG?
That's an important distinction to me that you basically can't -find- in the description of most supergroups. allow me to explain the difference as I see it.
In an ActiveRP SG you have players forming teams, running missions, and RPing as they do so. In-character interaction before and after the mission, witty banter flying about during fights, drama and comedy throughout.
In what is, apparently, the standard RPSG "Static" Roleplay seems to take the fore. Most people spend most of their time standing around in a bar, the base, or some other static environment and RP. Sometimes other RP goes on which leads to someone being taken to the Medbay or something of that nature, but generally RP is Standing around RP.
Now i have nothing -against- what I call StaticRP SGs. But they seem to have a higher propensity for cliques and Text-scrolling causing new people to feel out of place in some cases. The only thing i truly -hate- about the StaticRP SGs I've run with is the phrase "Read the Forums". My character should not have the information on the situation located on the forums. So reading them is a purely out of character exercise which leaves my character just as in the dark as she was before you told me, Out of Character, to go read the forums.
So what I'm looking for is ActiveRP Sgs or ActiveRPers looking to join such a group that I can then found.
Again, I have nothing against StaticRP sgs aside from the "Read the Forums" thing. Just looking for a more active one.
-Rachel-