They are still considered by the USDA and APHIS to be invasive and/ or pests. Captive breed or otherwise; I had my hopes high that the US wouldn't outlaw captive bred species; but alas…. It's interesting because most invasives come from coprate interest; expample the emerald ash borer came in the wood used for pallets or the "japanese beetle" came in on iris bulbs. Supposedly.
So exotics, no in state or between states. Captive bred or not. You can get a license or permit from APHIS, most will laugh that I even mention it though.
Native species can be sold in state, but I believe not between states.
If you want the permit site I can give you the link. From what I heard they are near impossible to get, and take many months if you do get one. The permit does not allow for sales of the species (each permit alots for up to three) unless the person you are selling to also has a permit for those species…..
Have I mentioned how let down I feel about our country lately? I mean writing all this just gives power to unreasonable laws. Its an on going joke between enthusiasts that tropical species could over winter, let alone become invasive… Rotten wood, major cash crop.