It's a lot of information there with different approaches. I basically threw it together for you. There's no doubt you'll have to put it in your own language. I didn't intend to write in terms of the 'sensitivity' of your manager.

You are right, you do not want to be perceived as challenging your manager. This is why the informed consent is the best approach to start out with as prescribed. Write it in your own language. You should also mention in writing your religious belief against vaccination. That's all that is needed to be said or should be said. Discussing your religious beliefs will be counter-productive.

As I stated in my posting, when submitting the informed consent, you'll know how this plays out before they even get back with you. You must get Informed Consent though. The questions conveyed are lawful and your life depends on it. If your management refuses to answer the questions, it's not hard to deduce you are going to be terminated. It may delay the inevitable though. The religious exemption, which is already has legal precedent, will most likely fail as well. They are violating the law, and your Rights.

In other words, you are experiencing coercion by your employer, which is also unlawful. It also violates every tenet of the Nuremberg Code. At this point, you must realize you are experiencing tyranny. I hope you recognize this. Your employer is selling you out to the enemy. There's no sense of being a nice guy at that point in time which you know you're going to be terminated. You are being thrown under the bus. If you have a family, then it is not only you, but your wife and kids too. Playing nice is not going to make this go away. Start out amicably despite management using coercion and putting you under duress. Try everything to negotiate a solution. Ask questions regarding Informed Consent. If you know its looking like termination, then educate management on what the existing laws are. An EO never eclipses and over rules legislated law or the Constitution.