Go to the EEOC website. Read the very specific criteria for religious exemption. Craft your request directly to those points. Do not stray, expound, nor try and justify. You do not have to -- just state. Be polite but use phrases such as "per EEOC guidelines ___" to let them know you have done your homework.

Most HR departments are just covering their asses against government prosecution and liability from lawsuits by litigious coworkers by placing the vaxx requirement on their employees as they believe they must and don't really give a shit about the shot. Help them help you by exactly checking the boxes that the EEOC sets forth. That is what they'll need to rebut pressure from above if ever challenged.

Edit: Spoken from experience. Got mine from a very liberal employer.

https://poal.co/s/TellPoal/442150/1a985e2c-2a35-4b7d-b473-3985ef868983#cmnts

At this link you are able to download Vaccine Religious Exemption documents. Use these for the COVID vaccine mandates if being required for work/school/military. https://defendingtherepublic.org/covid/

This site is also full of great information: America's Frontline Doctors at https://americasfrontlinedoctors.org/

Here is a page on the LAW regarding the vaccine: https://americasfrontlinedoctors.org/legal/ - includes sample letters and forms to use if one is being "required" to get vaxxed. NOTE the left-side navigation section with a bunch of legal-related resources, law suit cases. and documentation.

Peggy Hall is the best I am aware of she has extensive videos on the topics and solutions for practically every scenario, I picked one for you to check out, if its not 100% informative she has many more including Q&A ones also. GOOD LUCK !

https://www.youtube.com/watch?v=-7bmHoygqhc