As a liberal, I have some concerns with the idea they should be barred from exercising any constitutional rights.
My concern starts with the "no fly list" itself. How has it been created? What sorts of checks and balances are there regarding people who get listed? Are there any due process protections? Say, a right to know the evidence on which the listing is based? (Those charged with crimes have the right to "be confronted with the witnesses against him;" should those on the no-fly list have lesser rights?)
Let's look at the use of the no-fly list when it comes to other constitutionally protected rights*
Let's say 'you' somehow end up on the no fly list. Should your right to free speech be negated? Your rights against unreasonable searches and seizures? Your right to peaceably assemble with others? Your right "to petition the Government for a redress of grievances."
= = = =
* Note, I personally don't think the constitution confers an individual right to own arms, but the Supreme Court has declared otherwise.
And I recognize a certain absurdity with not allowing some folks to fly because they are potentially dangerous but letting them buy whatever firearms they want.
As 'they' say, "hard cases make bad law."
Perhaps this is an example?