Yeah, issuing the pass that doesn't differentiate between vaccinated and excluded would prevent almost all of the concern. Some people do have concerns about disclosuring health info to the government. Although the government could just buy the "anonymous" medical records and figure them out if they really wanted to.

Yeah, religious exclusions get tricky. Really the whole thing can be tricky because it comes down to philosophical beliefs of what should be mandated and for whom.

Edit: Why so many downvotes without reply?