This would become quite a thorny constitutional issue very quickly. The 14th amendment explicitly specifies that one state can’t try to prosecute someone for something done in another state that was legal there but is illegal here. This has further been interpreted to mean that interstate travel as a whole is a protected right, and any form of checkpoint or other hassle-station on a border between states would surely also be a 4th amendment violation.

That’s not to say some idiot won’t try it eventually, especially given the current political climate, but up until now it’s not done as a matter of course.

A state neighboring mine got in big time hot water a decade or so ago for stationing their own cops in our state and tailing people out of liquor store parking lots with the aim of harassing them over the minutiae of the differences in liquor laws between the two. Obviously that didn’t fly, because that state does not have jurisdiction here which means they have no grounds for a stop or search. Likewise, entering another state is not legal grounds for a stop and search unless that state’s law enforcement already has some manner of articulable probable cause.