I don’t know where you daven, but where I daven (quite a yeshivishe place), the person sans hat and jacket is welcome (although IMO he’s wrong for not conforming to minhag hamakom),
Sometimes for Shabbos i visit relatives from such communities and I dont even own a hat. It is quite clear from my appearence that I am not one of them. Nobody has ever said a word to me about not wearing a hat (Only a shul near my house had such a rule ) and many times they come up and say hello.