You really think it would only be fair that BMG and Bobov and Brisk and Ponovoze should allow a guy in a colored shirt to daven for the amud on Shabbos?
You ask that like it makes sense or something.
If someone who wears a white shirt came in dressed in weekday clothes or in a colored shirt, I would have questions. But if someone comes in in a shabbosdik colored shirt, does that automatically interfere with their level of ehrlichkite? I would have no problem with the shul making a “white shirt” policy if they also are very makpid on not allowing anyone who has been indicted, arrested, withheld a get for any reason, is rumored to have abused anyone etc. I believe that what is so offensive to some is the assumption that just wearing a white shirt implies more than it really does. If it is not part of a whole Torah lifestyle, it is nothing at all.