DaMoshe,
A person shouldn’t be judged on clothes. They should be judged on whether they are a good, frum Jew, with yiras shamayim.
I absolutely agree with every word you wrote.
I don’t think that a shul having a policy that anyone davening for the amud should wear a hat and jacket violates the above statements, however. You yourself provided the best reason by writing:
Remember, however, that the halachah is that a person should dress respectfully when davening, as they are speaking to Hashem
Different communities and shuls will have different definitions for dressing respectfully. You may disagree with their definition, and that is fine, but they have a right to their own definitions, and they have a right for their customs to be respected. Would you go to Japan and take offense from an innkeeper who won’t let you walk on his tatami floors because you have your shoes on? Or would you just take your shoes off and go in? I understand that this situation feels different because of the perception that your own culture is being degraded, but I honestly think that that unfortunate circumstance arose due to mistakes made by the people you interacted with, not the policy itself. Would it cause you harm to don a hat and jacket (or even a black velvet kippa) if you really wanted to daven for the amud at this shul?
The Baal Tefillah took off his hat and put the talis over his head. Shabbos morning, married men usually don’t wear hats, as they have a talis on.
I thought this story was regarding Friday mincha/Kabbalos Shabbos? Perhaps the shul would have no problem with you davening for the amud if you covered your head with a tallis too?