I thank people for their service here and see the military as a necessity. But when anything like this has to be passed through the filter of "national security and risk to military service and intelligence" red flags go up all over. I do see that sort of thought as very political for a number of reasons.
Our history of the use of our military is far from all positive. The complex of industry, government, military and intelligence that exists to drive activities based on security is also highly questionable at times. Objectivity and truth is likely very hard to arrive at within this area because the system itself is not served by any such scrutiny. The old horses of "national pride and honor" also make appearances in this part of society and those too should be looked at with skepticism.
I'm a citizen, but i'm no patriot, but even with that bias, i understand the need for un-shared intelligence and confidentiality in some parts of public service. However from what i have seen on what she has leaked, there not does not seem to be a lot human damage, but there is a fair amount of political embarrassment, and talk of transparency etc
For these reasons, i would support the President's action whether she was trans or not.