I don't recall any questions about foods/trash/alcohol when going between BVI and USVI. If any are asked the correct answer is a firm no.

Last year we had two Europeans aboard. As I recall entry into the US by "private vessel" (boat or aircraft) is different than by common carrier. Because their first entry point into the US was not by common carrier they needed visas as the reciprocal agreements do not apply. I'm sure others here can help if I got any of this wrong.