Tsk, now that's a project. It is possible, and actually very easy; however, it is an extremely time-consuming process.
To go about it PERFECTLY, you would need to change the costume .pcs file with the file replacement code. For example:
Sonic:
Get FitSonic00.pac from wherever (mediafire, the iso itself, whatever) and rename it to the read team's number (check the texture thread for that information). Put it in SD:/private/wii/app/RSBE/pf/fighter/sonic/. If you want to really go for it, open common5.pac and swap the portraits, stock icons, then go to your .brres battle portraits and rename them to swap them, etc. etc. Repeat for victory portraits. That will make Red Team pick blue Sonic.
Do the same for the rest you want to change. It's simple because you don't need to make anything new, but it's a lot of work.