Your constitutional carry argument is not relevant. It’s not a matter of personal responsibility, using fake vaccination cards is crime with real consequences for innocent 3rd parties.
Enforcing health measures is neither new nor constitutionally unreasonable. Whether masks, vaccinations, or sanitation standards. By your standards why should cooks or food handlers be forced to wash their hands ?
Are you ok with the person cooking your lunch lying about washing their hands after wiping their ass ?
Citing things proposed in NYC is a straw man. NYC is both the extreme of authoritarianism in most things and has conditions and population denote not found elsewhere.
Intentionally coughing on people is assault which means both violent response in self defense and arrest are appropriate counters.