But it is... The military integrated long before the rest of society did. Women worked factory jobs to support the military before it was widely acceptable for women to work. The military is an avenue of social change. It provides the most unbiased look (as compared to the alternatives) at how things will work mainly because we value mission accomplishment above all else. It is a solid baseline that can be evaluated against. Pretty much nothing else in society gives you that.
See that is my main problem with using the military as a vehicle for social change. The way it seems to occur in the present era does not strike me as an effort towards readiness and mission accomplishment. It seems to be a way to make politicians feel better. For example different physical standards don't seem to be about mission accomplishment to me, they seem to be about making it a more inclusive military.
Not all social change is bad, I am certainly not arguing that there is nothing that the military should change. However, integrating fast attack submarines just doesn't seem like a good idea to me because of the major ass pain it would entail and a huge push to do so in my mind is driven by something other than mission accomplishment.