Inspired by this answer, do vaccine mandates amount to religious discrimination? Could a restaurant refuse to serve unvaccinated individuals, even including those with sincere religiously-founded anti-vax beliefs? What about if this mandate is just company policy, not legally required?
Do vaccine mandates amount to religious discrimination?
The term "vaccine mandate" is not sufficiently clear to tell, in a vacuum. Is it a mandate to get a vaccine? A mandate not to serve an unvaccinated individual in a public place? A mandate to vaccinate children that attend public schools? A mandate to serve unvaccinated individuals at public accommodations? Or what?
The details of the mandate, how it was enacted, and the circumstances under which it is being challenged, are all critical to determining its legal validity.
As noted in the linked answer (text reordered for clarity):
Under the US Constitution, a public health authority could even make vaccination mandatory, and this was done in some historical epidemics.
In Jacobson v. Massachusetts, 197 U.S. 11 (1905), the US Supreme court held such mandatory vaccinations to be constitutional. . . . In Zucht v. King, 260 U.S. 174 (1922) the US Supreme Court upheld as constitutional a public school district's exclusion of unvaccinated students. . . . In Compagnie Francaise de Navigation a Vapeur v. Louisiana Board of Health, 186 U.S. 380 (1902) the US Supreme Court upheld as constitutional an involuntary quarantine law.
Likewise, facially neutral health and safety regulations of businesses are generally valid even if they disproportionately impact members of a religion, under the First Amendment to the U.S. Constitution (and as it is applies to state and local governments under the 14th Amendment to the U.S. Constitution).
The Religious Freedom Restoration Act of 1993 tips the balance somewhat to make accommodations in some circumstances to facially neutral laws that disproportionately impact the free exercise of religion, but still does not prohibit facially neutral laws that serve a compelling public purpose from burdening the free exercise of religion. The core language of that Act which sets forth the substantive standard in those cases states that:
SEC. 3. FREE EXERCISE OF RELIGION PROTECTED.
(a) IN GENERAL.—Government shall not substantially burden a person's exercise of religion even if the burden results from a rule of general applicability, except as provided in subsection (b).
(b) EXCEPTION.—Government may substantially burden a person's exercise of religion only if it demonstrates that application of the burden to the person—
(1) is in furtherance of a compelling governmental interest;
(2) is the least restrictive means of furthering that compelling governmental interest.
(c) JUDICIAL RELIEF.— A person whose religious exercise has been burdened in violation of this section may assert that violation as a claim or defense in a judicial proceeding and obtain appropriate relief against a government. Standing to assert a claim or defense under this section shall be governed by the general rules of standing under article III of the Constitution.
The standards referenced in the act tap into well established case law that was previously applied less broadly than under the Act, when the U.S. Constitution alone, unaided by the Act, was implicated.
Could a restaurant refuse to serve unvaccinated individuals, even including those with sincere religiously-founded anti-vax beliefs?
Usually, businesses can establish facially neutral rules even if they have a disparate religious impact. Generally, private businesses do not have an affirmative duty to serve anyone.
Certainly, it could do so as a matter of company policy, if the law did not forbid discrimination specifically on vaccination status (which it currently does not in most or all places in the U.S., although there may be recent legislation on this of which I am not aware).
For example, it is legal to operate a restaurant that only serves bacon cheeseburgers and operates 7 days a week, all year long, without holidays (in many places that lack blue laws for restaurants), even though this effectively denies service to strictly observant Jews, Muslims, Hindus, and (on Fridays during Lent) to observant Catholics, and could make it an uncomfortable place for such workers to work.
The harder question is whether the restaurant could serve an unvaxxed individual when the business and the customer both want to do so, and both have sincere religious beliefs that cause them to feel that they must do so (the business owner might have sincere beliefs about serving everything, the customer might have sincere beliefs about being unvaxxed for religious reasons).
Even then, when religious people aren't singled out for being religious, this requirement might be upheld if there was no alternative that meets the public health goals of the requirement, although the case that there could be some alternative that is less restrictive might be pretty good.