I would think that the Olympics committee should concern itself more with official national requests rather than popular uproar.
If a significant percentage of Olympic nations request a change in date then the committee should consider and vote on it. It's far enough in advance to avoid being a scheduling hassal.
Heck, if a quarter of the participants in almost any event request a change in date it's usually granted to them so long as it doesn't pose a problem for anyone else.

Why not give it to them? No reason to say "no" just because they're muslim.