If you can’t see the difference without help nobody can explain it to you.
Tell me what you think the difference might be. Also tell me why you think the courts will decide it’s different. I agree that the current Covid vaccines suck, but I don’t see their suckiness making enough difference to overrule a direct order of the Commander in Chief (or your commanding officer).
The judge’s assertion that the Constitution isn’t suspended while you are in the military is clearly incorrect. The first right you lose is freedom of speech. The UCMJ is the controlling document for military personnel. While you may not lose the right to your choice of religion, you are not allowed to practice it where and when you choose.
Lose the ad hominem and explain your opinion.