It doesn't result from female privilege, it is considered a non-issue and discounted because of female privilege. There is plenty of evidence to support that, including the fact that FGM is considered a larger issue although it has effectively been eliminated in the west.

Consider this, if a father wanted to have his newborn daughters' clitoral hood removed because he didn't like the way it looked, he would be rightly ignored. If a mother wants to have her newborn son circumcised because she doesn't like the way uncut penises look, he will be circumcised. No matter how you want to slice it, both are genital mutilations. The difference is, one is ridiculous, uncommon and illegal, and the other is ridiculous, common, legal, and widespread.

Female genital mutilation is pretty explicitly about controlling female sexuality in a way that makes women more obedient male property.

It does happen almost exclusively in Islamic areas, and some religious leaders do mandate it, so I'm not too sure about that. In any case, religion is a poor reason to justify mutilation. Circumcision was performed on male slaves to make them "less likely to rape white women", so I also am not too sure about the underlying reason for male circumcision. Both practices seem kind of barbaric.

Circumcision, though, seems to be a religious thing from a very patriarchal culture. The modern justification for which is hygiene and/or health, and sometimes it's definitely medically necessary.

The hygiene and health arguments are bogus, and have been proven to be bogus. If women were having parts of sexual organs removed for "hygiene" reasons, it would not continue for a moment.

So I'm not seeing how circumcision is evidence of a gender power differential.

The fact that nobody questions male circumcision which is forced on over 50% of males born in the United States today, while FGM, which is much less widespread largely occurring only in Africa and the middle east, garners considerable attention provides evidence of a power differential. It clearly shows that male health issues are undervalued, even in relation to obscure female issues, reinforcing the matriarchal view that men are inherently less valuable than women.