I think it is very noble of you that you make a last stand. However, my advice is that you should seek an exemption from the government if you want to stay on. Can you file an exemption at your current workplace?
Are you a civilian worker or a contractor? I don't think as a contractor you have much choice in exemption. The funny part is when I was working as a contractor last year, I asked the government about it and they said unless the vaccine is in the contract, they can't enforce any sort of mandates or vaccine. It seems like now they didn't do that. I wonder if there is a plausible lawsuit? Because the government could say the vaccine isn't a mandate of the contract but part of the entrance to the base or area you're working in.
Either way I would first try the exemption route. Then, unfortunately I don't think you're going to get unemployment if you were fired with cause. As the other poster said it is within the unemployment requirements that you be let go of through no fault of yours. By refusing the vaccine, that could get you. That's why I think the exemption route is important. You have document proof that you tried to file an exemption and you can go to the unemployment office and the employer would have to state that you tried to get an exemption and they refused and still let you go. That might entitle you for unemployment because you could say that the exemption was for valid reasons.