Although I certainly can't speak for literally every aircraft, I have never seen an actual restriction from the manufacturer with respect to crosswind. Every POH I've ever seen says it's a maximum demonstrated crosswind. Which is not a regulatory restriction. I just double checked that, and it was true of the 737NG series in revision 29 of the AFM and the B744 in revision 42. Although to be fair the wording used is somewhat confusing because it says the maximum demonstrated crosswind is X but this is not "considered to be limiting" on a dry runway with all engines operating.

I know there are some aircraft equipped with some engines where there actually is a hard AFM limit on crosswind, which is usually related to engine performance (some engines can experience compressor stalls with a strong enough crosswind component), and of course operational manuals issued by airlines generally have limits to be obeyed by their pilots which are often but not always constrained by the maximum demonstrated crosswind. For example, in 2002 Continental was telling their 777 pilots that they could land with a 45 knot crosswind on a dry runway and a 40 knot crosswind on a wet runway even though the manufacturer's demonstrated crosswind was only 38 knots.