So I have a guardian's theme team with Venom Rocket Raccoon. And he activates his trait.

CALL IN HELP FROM THE VENOMVERSE!: Once per turn for all characters with this trait, when Venom Rocket Raccoon hits an opposing character, after resolutions you may roll a d6. 3-6: Place another friendly character whose name includes "Venom" adjacent to Venom Rocket Raccoon.

And I pick a Venom that isn't Guardian's Flash Thompson Venom. Do I stop being a theme team and therefore can't use TTPC anymore? I'm sure I couldn't use said venom to TTPC, but does it disable the entire team for being there?

I think everyone will be confused by your question. Are you assuming that the trait allow you to put in a character from your sideline?

If that is your reading, go back. The power says nothing about getting a figure from outside the game - the figure come from another spot in the map.

Ah, that solves the whole thing. I was thinking it was a sideline effect. Simple error in reading. Well that clears that up. Well sorta. There's other characters that could bring a character in from the sideline that doesn't have a keyword. So bad example, but doesn't solve my problem.

This does raise the question, do the BTAS TroubAlert chases break theme team when they’re called in?

Theme is determined at force construction, once, determined it does not matter.

To double up on this: from the rulebook p 33:

Well that's helpful. No matter how many times I read that thing it amazes me how many things I miss... or more likely don't think about because I don't think it'll ever come up. Then it does.