You are definitely not a libertarian.
You can also enjoy yourself and not worry about getting covid even if you don't have the vaccine. Those that have the vaccine are protected from those that don't, and those that don't are choosing not to get it at their own risk. If a vast majority of society gets the vaccine (already happening in US, is the case in Israel) then it significantly slows the spread and it becomes endemic. Young and healthy people literally have greater than 99.99% chance of survival. To continue treating this like it's a grave threat to everyone's life is just mindless paranoia.
How is it not the right of a private business owner to set the conditions for entry onto their premises?
It is, I didn't say it wasn't.
The policy itself is immoral. It should not be encouraged, even though they can do it. Good businesses should not do it, and I think good libertarians should vocally oppose it wherever it happens.
You could also make a case that this is business collecting information and colluding directly with the government, so it violates certain privacy protections that have precedent. Regardless, "Muh private business" does not excuse bad actions. You can have policy and you can have values. Private businesses performing authoritarian acts should not get praise from any libertarian.
Stopping the spread of a disease is “authoritarian” lol