Sam2,
So acknowledging that reality, I realize that it is disgustingly Chutzpah-dik to wear a hat into some DL shuls. They don’t feel he’s better than them. They feel that he holds himself as better than them because he wears a hat.
I do not have experience with these conflicts that you are describing, but your conclusion here does not make sense to me. If a person goes into a shul to daven, then it follows that he considers it advantageous to “package” his tefillos with those of the mispallelim there, and that they are kosher for a minyan. Therefore, it would seem to me to be the opposite of disrespect for a chareidi to take his hat and jacket into a DL shul to daven.