I’m sure there’s a rule that makes it illegal for interstate travel to be influenced by one state over another. However, that would require the federal government to do something about it. Or someone filing a case in the federal court.
The Heritage Foundation addressed this in "Can States Restrict Travelers From Other States?" on April 10, 2020
States have “police power,” the broad authority to do what is necessary to provide for their people’s general health and welfare. But there are two relevant limitations on that power: the commerce clause and the privileges and immunities clause.How ironic it would be if SCOTUS upheld the states rights to ban entry of immigrants on health and disease grounds. It would vindicate President Trump's remark in the summer of 2015 that they "aren't sending us their best."Both can be thought of as anti-discrimination rules. The commerce clause (by judicial interpretation, not its text) prevents states from discriminating against the commerce of other states, and the privileges and immunities clause prevents states from discriminating against the citizens of other states. It also protects the right to travel between the states from unreasonable restrictions.
The Supreme Court has long upheld quarantine laws against commerce clause challenges. In Oregon-Washington Railroad v. Washington (1926), for example, the Supreme Court recognized that “it is well settled that a state, in the exercise of its police power, may establish quarantines against human beings, or animals, or plants” that may spread disease to the state even if those quarantines negatively affect interstate commerce.