I can totally understand this point of view. It would be very tough to serve in the military and repeat lies you don't believe and refuse to teach your own children.
But remember the private sector is probably nearly as bad as the military when it comes to being "woke". With the military you will have some job security where as in the private sector you will be thrown out the moment they can replace you with a cheaper option.
Just something to consider.
I've been out for a few years now and working in the private sector since then, unfortunately at one of the worst massive globohomo corporations. The money is good, my particular job doesn't require me to sacrifice my principles (we do get weekly emails haranguing us about some woke initiative or other and active participation is rewarded but not yet required), and I am actively working to free myself and my family from their shackles via crypto, real estate investing, and a side business which I expect to be able to accomplish in the next 5 years. Ironically going back in the reserves will help speed that process up as well from a financial perspective in a number of ways. So going back in even the woke military won't really be any worse than my day job from a SJW perspective, other than in the sense that I expect better from the military. And I do think it's important for us to maintain a presence on the inside of the military as well as other important institutions (the financial sector, media, other large corporations, government bureaucracy, all levels of law enforcement, even the 3 letter agencies) for a number of reasons.