For the most part, one should dress in a way that resembles everyone else unless one is making a statement by dressing differently than everyone else. If you don’t want your clothing to indicate an ideological position, dress in a way that fits in. This applies in general, not just shul.
TO bring down a non-religious example, a man should normally wear pants unless he is a Scot making a political statement by wearing a kilt, or an Arab wearing an ankle length gown in a place wear everyone else dresses “western”. If you are in a shul in which most people wear black fedoras, wearing no hat other than a kippah, or on the other hand wearing a homburg or a streimel, communicates an “agenda”. That’s good if that’s what you intent, but not if your intention is just be normal and not make a statement.