1. Make Sure Your Activity Online And In Real Life Is Not Inconsistent With Your Exemption Request
Under Title VII, your employer only has to consider accommodating a "sincerely held" religious belief. While generally, pretty much any belief is presumed to b sincere, if your behavior or actions suggest that your claimed belief is not sincere, then your employer can lawfully deny your exemption request. For instance, let's say that you talk with your co-workers and/or on social media about how you don't believe in any religion at all and how you are convinced that God doesn't exist, etc... If your employer becomes aware of those claims, they will have legitimate reasons to doubt the sincerety of the religion that forms the basis for your exemption request.
Likewise, you should avoid making it sound like the reason you do not want to get vaccinated is because you doubt the safety or effiacy of vaccines, or for any other political / scientific reason. While you may or may not be right about anything relating to Covid-19 vaccines, these types of claims will, again, call into question the real reason for your exemption request. Remember - your employer doesn't have a legal obligation to consider granting you exemption from vaccination requirement based on how you feel about vaccines, what you learned about them from various soources, and how much or how little you trust the "system". They only have to accommodate your religious belief.
2. Be Flexible In Your Discussions Re Accommodating Your Religious Exemption Request
Like in any other type of negotiation, you should be ready to be flexible when discussing the exemption issue wtih your employer. It is perfectly appropriate to negotiate an accommodation solution that, while might not be perfect, is acceptable to both you and your employer. For instance, if your employer grants you exemption based on your religiou but they require you to get tested every week, you could ask for less frequent testing of perhaps every two weeks. In the end, you may agree on getting tested every 10 days, which will save you from one extra test a month. Your employer might insist that if you are unable to get vaccinated, you have to work 100% remotely, while you may want to do some work form the office. One simple solution to this issue could be allowing you to be in the office during hgorus when everyone else is away, or designating a separate area in the office for you that will allow you to mihimize unnecessary contact with others. In any event, neither side should approach the accommodions process as "it's either my way or no way". Further, any accoommodation agreed upon can be reviewed and re-evaluted as time goes by and as all the surrounding circumstances evolve.
Whether your employer will or will not grant your exemption request will depend on other factors, including their general approach and flexibility when it comes to this issue, but keeping the above two factors in mind will go a long way toward making sure that you take the right steps on your end of that process.