.. that sounds like a dangerous road to go down.
Australia has tried to "force" vaccines for years - if kids are vaccinated the parents get worse tax breaks, kids can't goto daycare or elementary school, etc. but AFAIK it's not a "legal" requirement, and nobody can be terminated from employment.
People who have been vaccinated themselves will not care if the police they have to interact with are vaccinated or not (well, 95%ish not care).
People who have not been vaccinated should err on the side of assuming anyone they come in contact with is not vaccinated (and is possibly infected) anyway, and should take precautions.
No, that's not perfect, because precautions can still fail to work, but it's not absolutely the worst either.
On the flip side, I don't think it would be unreasonable to have police (etc.) who refuse the vaccine temporarily reassigned to roles that limit their interaction with the public.