AS far as I could tell, the Tudors kept trying to make themselves ‘more’ than just a king/Queen, but tried to make themselves popes and eventually Gods. The Plantagenet were on good terms with the other royal families of Europe and were questionably accepted by the other dynasties. They were the closest descendents of William the Conqueror and it’s telling that after Henry VIII treated his first wife horrifically, the more prominent dynasties didn’t have much to do with them in regards to marriage.
It’s very true that European royalty was very wary of the Tudors. I believe Ferdinand and Isabella were leery of sending Catherine over originally. Thank God, as bad as he treated her, Henry VIII didn’t murder her.
Of course, Henry VIII had Plantagenent blood in him - his grandfather was Edward IV and he looked quite like him. But in all other respects, he differed from that rascally but laid-back Clintonesque king, lol!