I mostly disagree.

First - it is the US government - not the US military that supports the Saudi regime and made whatever policies regarding which governments to support. I'll suggest that most US military personnel, on a personal level, are probably uncomfortable with the support for some regimes, particularly Saudi Arabia. It is you the American voter - that de-facto keeps that policy in place - not the US military.

Second - it's wrong to suggest that because the USA favoured 'right wing' or 'left wing' governments somehow equates to the 'oppression of women' and it does not stand up to scrutiny.

Russia, Poland, Croatia, Ukraine, Lithuania, Latvia, Estonia, Moldova, Czech, Slovakia, Montenegro, Hungary, Bosnia, Serbia, Macedonia, Bulgaria, Romania, Belarus, Tajikistan, Afghanistan, Turkministan, Khazaktstan, Vietnam, Cambodia, China, Cuba ... arguably Venezuela ...

Shall I go on?

This 'short list', comprising maybe 1/4 of the planet - are of countries where totalitarian leftist regimes have viciously oppressed everyone's rights in the name of a 'glorious egalitarian ideology' and let their people rot in ruin.

In almost every scenario of American intervention, there is a pretty high degree of moral ambiguity. A Chilean Communist, with only 30% of the vote, who invites the Soviets to come in support his total takeover and to impose their version of soviet-style socialism, is hardly a situation of moral progress on the part of such leftists. After US intervention, the US backed right-wing Pinochet tortured 3K people and killed 300 on his path to power, which is obviously terrible, but it might very well have been the far less evil choice of two evils. It's wrong to imply that a soviet backed, non-populist communist takeover of such a country would have yielded much better - and probably worse.

"Furthermore, the united States military's strong internal structure of subservience to upper commanders and reliance on internal courts has led to a culture of sexual violence unpunished."

1) 'Subservience to upper commanders' is a military thing, not a US military thing, and it's a fundamental part of the equation.

2) This is not what led to a culture of sexual violence - moreover, the US military does not have a greater level of sexual violence than many other institutions - the US military does have a group of very aggressive people (by design) which will lead to more negative outcomes. It's very good that things are getting better, but your analysis I think is off.

"What about the support of sexist regimes such as Saudi Arabia?"

Even a very simplistic geopolitical assessment of the situation answers your question quite readily. The only pragmatic option for Saudi right now is a) House of Saud or b) total chaos w/ISIS etc.. There is absolutely no 'movement' of progressives in Saudi Arabia of sufficient popular influence or power to even contemplate a secular government as we might expect in the West. There are competing houses, a somewhat oppressed Shia minority who would love to rise up and mass murder their perceive oppressors (with the help of Iran). Even in a moderately more secular country such as Syria - we can see what happens when there is instability: there is no clear path out of that Pandoras box.

Also - overwhelming majorities of people in that region support most prevailing cultural institutions such as how women are to dress and act etc. Who are you but a Western Imperialist to decided for them what is appropriate and not? Given a vote, you'd be surprised at what many people would chose. It would be far, far more conservative (in the sense of 'traditional') than most progressives would be comfortable with.

Anyhow - it's besides the point. Those policies are chosen by your elected representatives, not the military.