You might say that airlines, as private businesses, should be allowed to choose not to transport anyone they wish. But this shouldn’t be viewed as private action, it is state action. The proposal comes in response to an FAA threat that airlines had one week to come up with a solution to unruly passengers.
There is a federal regulation in place on masking. That has a fine as a maximum penalty. Pressuring airlines to impose a more significant penalty than provided for in regulation or law is highly problematic.