I hate to use this analogy but just wondering if you were offered a job paying $200,000/year and where you were only allowed to wear solid black/blue/grey suits and white shirts, would you turn down the offer?
DY: I agree that it is not a minhag. At the same time it may be a mishegas. But a yeshiva is allowed to set a policy even if one disagrees with it. You have a right not to send to that yeshiva. My oldest switched to the main Chafetz Chaim branch for his sophomore year; not because of the colored shirts but it was the yeshiva we thought he would find hatzlacha in his learning. We thank HKBH for instilling us with the insight to make that decision as it has turned out to be a good decision.
As to YTY switching policy, I do not recall that any other Brooklyn yeshiva putting pressure on them to change. They decided on their own what to do.