Got it, can states/airports decide unilaterally not to serve them? I imagine if the highest volume airports banned these flights it would ground the vast majority of them
No? FAA makes these decisions.
Yes, an airport could reject any flightplan filed with type B38M or B39M citing operational reasons. The exception to this in the USA is when the airport is in receipt of FAA improvement grants, when they are obliged to accept all compatible traffic.
Or more subtly adjust landing and handling fees to astronomical levels for those types. That's how Gatwick in the UK discourages small turboprops, for example.