I read somewhere that the 14th amendment requires states to respect each other's drivers licenses. If so, that should also apply to CCW licenses.
No, not amendment 14, but article 4, section 1. Maybe a dyslexic person told you that? It’s unclear which way that might go. If Florida fully respected New York’s laws, I wouldn’t be able to carry there. OTOH, if they fully respected our laws, I would.
Anyway, concealed weapons permits are not mutually recognized among all states, but many states have reciprocity agreements and recognize each others’ permits.