Egypt’s military already stepped in once to toss the brotherhood out, and they are the most stable group in Egypt. They also have some respect for Israel.
Surrounded as Israel is, a questionable ally may be better than none at all.
Which could rapidly change. I’m sure you’ve heard the Egyptians have been fighting the extremists in Sinai for months now.
The extremists in Sinai have plenty of friends throughout Egypt, all those Muslim Brotherhood supporters for example.
Egypt isn’t that stable.