Religious exemption requires letter signed by a clergy member.
Says who?
Is that a federal thing, a state-specific requirement, your employer's requirement, or what?
I know several people who got a religious exemption without a clergy member.
If a clergy member is required, one can use Bp. Athanasius Schneider's exemption, listed above.
BTW, some are saying "SSPX won't do it", but some SSPX priests will. They are not all agreed on it.