I absolutely agree with Sandtiger. It's not just a hypothetical risk, either; the fish viral disease KHV and the amphibian fungal disease Bd have both been transferred from captive to wild populations, where they are causing mass die-offs, and in the case of Bd, extinctions.
In Tennessee a major reason behind the new collecting regulations is to keep people from introducing fish to different drainages. In many cases the fish in one stream include different but related species from the fish in the adjacent stream; if you innocently collect some fish for bait or pets and then release them into a nearby stream, not the one you originally collected them from, you could introduce a competitor or cause hybridization to occur. This would eventually lead to homogenization of the stream fauna across the region, and we would lose a lot of species diversity. Tennessee has well over 300 fish species, and nearly a third of them have some kind of conservation status.
Which is not to say I entirely agree with the new regulations. They go too far in impinging the rights of native fish keepers, and not far enough to prevent bait bucket introductions, in my opinion.