Is there anything that can happen to your active pet in terms of random events and color/species changes?

I'd like to keep the pet I'm currently training as my main battler active, but I recently turned him into a fairly expensive color and species (angelic aeanoid) and don't really want him getting changed.

Nope. There is an event now that gives you the OPTION to change your pet into a Bumbus, and a few events that will add stats or Treasure Chest slots, but there aren't any that change their color or gender.

That's comforting to know! Thank you!