No, it is not illegal for businesses to require proof of vaccination

If a person refuses to disclose their vaccination status, a business cannot search their pockets or vehicle for proof they are vaccinated. However, it can ask for the information to be voluntarily disclosed. If it isn’t, a business has the right to refuse entry, according to Michele Goodwin, a [Chancellor’s] professor of law at UC Irvine and director of the Center for Biotechnology and Global Health Policy. “Businesses can establish standards for entry that do not violate statutory or constitutional provisions in a state or federal law,” Goodwin said. “The Fourth Amendment applies to government.”