Eating exotic mammals would be less bad if the mammals and their meat were actually subject to the same health regulations as less-exotic mammals. That is: the problem ain't the animals themselves, but rather that they're being sold in a black or grey market instead of through more legitimate channels.

This is a pretty common theme with black markets in general, on that note. See also: black market drugs being "cut" with harmful substances, black market sex labor being a vector for human trafficking and STDs, black market medical procedures being more susceptible to adverse outcomes, etc.

There are other good reasons to not eat exotic mammals, of course (i.e. if doing so puts species at risk of extinction), but the sanitation issue seems solvable.