Never ever ask for an exemption. If you ask you are giving them permission to say "No".

You have to apply for an exception otherwise you're gated outside of the country.

If they ask how you are exempt you say for religious reasons. If they ask what your religion is you tell them you choose to not disclose that for fear of persecution.

I don't see this going well either. The criteria are:

1. The applicant must be opposed to all vaccinations in any form.
2. The objection must be based on religious beliefs or moral convictions.
3. The religious belief or moral conviction must be sincere.