There are almost three million Muslims in the UK, and I've never actually heard of many problems between Muslims and gay people, except gay Muslims. Polls show while many would not accept their own children as gay, they don't care what non Muslims do, and are happy with gay rights generally being applied.
Realistically, the number we'll take will be in the tens of thousands, and they won't all be Muslim, so it won't make a huge difference at all.
So yes, you're overreacting, stop making everything about you.