"but it's certainly not a protected right"
Everything is a right until the government decides to take it away, not just things in the bill of rights or codified by law. The government has to have a good reason to take away any right. Hamilton initially didn't want a bill of rights because he didn't want people getting the very idea that you have.
"Nor shall any State deprive any person of life, liberty, or property, without due process of law." Being able to travel on a plane is a form of liberty that virtually everyone has. Having that taken away without due process or even a means of appeal, which is exactly what is happening here, is illegal. Airplane hijackings account for a ridiculously small percent of deaths, but we spend more on stopping those than most other things. It's nonsense, and it's unconstitutional.