I think a distinction needs to be made between rescue and adoption. Rescue meaning you take it, rehabilitate it, to make it available for adoption. Too many people use the word 'rescue' to sound more official or somehow more righteous, when they're really adopting. I wouldn't go to the SPCA, adopt a dog and then claim I rescued it. The 'rescuing' was done long before I got involved.
Every state to my knowledge has specific laws for doing native wildlife rescues. People need to be licensed by the state, some by the USDA... but it varies by species. In Texas one would need a license to rehabilitate say, raccoons, but not necessarily snakes... but if you have a rehabilitator's license, you can rehab endangered/threatened species like indigos. Most states have specific rules that wild life rescuers do have to follow, minimal human contact, release sites, and so forth.
Now, exotic rescues - they are for the most part unrestricted. Again, it can vary by animal and state. One can't just become a tiger rescue, they have to be permitted by the USDA... but where I live, I can rescue all the burmese pythons or iguanas I want without any issues.
Laws in the US vary a lot from state to state, county to county, city to city... anyone looking into that sort of thing needs to be careful and do their research.
Rav