I have the same problem and whichever team I open with I have to select the other team and either start a character from that team or immediately switch back to the first team and then I can play. This started after the last major upgrade, I had no problem like this before then.
Lately the only characters is the zombie that gives me the start up problem. I can start in plant mode without being stuck in character select and have to transfer. When I start in zombie mode then I have to switch to plants in order to get out of the character select mode. After I switch from zombie to plant I can immediately switch back and everything is working correctly. My solution is to always shut down the game in plant mode and then when I restart it will open in plant mode and all works properly. Still a minor pain to go through.
