Even in considering moral questions it is often useful to consider some legal principles. The law is not always an ass.
In order to establish that one has a right to impose a curtailment of a right on others, the law often requires the imposer, such as the government, to establish that it has made all reasonable efforts to accommodate the other person. I think that is a reasonable principle.
Where a person claims to have a religious right to decline to take any of the Covid-19 vaccines and it is determined that in the circumstances an important freedom, such as the right to security of the person, or the right to dignity, can be overridden in the circumstances, society or the government as its representative, has a duty to provide reasonable accommodation for abridging the freedom. That does not mean it must cave in to all of the demands of the resisters, no matter how unreasonable. Resisters must be reasonable as well. For example, society could be required to accept an alternative to compulsory vaccination in some circumstances, such as providing that the supplicant for an exemption could be given the right to provide a recent Covid-19 test that reasonably establishes that the applicant is not a carrier of Covid-19. That is the course of action Manitoba has followed in its mandates for Health care workers to be vaccinated or get frequently tested. Other jurisdictions have been harsher. Some have been more gentle. Who is right? It depends on how important it is to have people vaccinated and how effective the tests are compared to the vaccines.
I think looking at the analogy of expropriation might be helpful. We have a society where each of is entitled to own property to the exclusion of others. That is called the right to private property. It is a very important right, but that right is never absolute. Government has the right to expropriate private property (which really means to take it) provided it pays fair value, actually needs the property and follows the rules of fairness. It is always important to remember that any right, no matter how sacred, is not absolute.
Doctors Manitoba has some helpful suggestions for accommodations : “frequent testing, continued use of protective gear and physical distancing or barriers to separate them from other workers.” That seems pretty fair to me.
Such reasonable accommodation could be required to get judicial approval or moral approval for imposing a vaccine mandate. This could be required if it can be established that the Covid-19 testing was reasonably reliable enough to warrant society being required to accept such a test result and may not require the applicant to get vaccinated as a result.
A government should always make reasonable efforts to accommodate people whose rights are being abridged. Sometimes however, reasonable accommodation just won’t be possible.