There is now a strong legal precedence for this. In creating the “right” of gay marriage, did not the SCOTUS use reciprocity as the rationale for extending it to all states?
Probably not. The Obergfell decision claimed that the 14th Amendment provided homosexuals the right to marry under due process and equal protection laws. We can debate all day the merits of that decision, and probably agree all the way, but this is not a 14th Amendment decision. The right to keep and bear arms is not being denied in any state. But the Supreme Court has also said, in Heller and other decisions, that states have the right to regulate gun ownership to a certain extent. A bill like this strips them of that power. So this is a 10th Amendment question and not a 14th Amendment one.