I'm sure people have also quoted this in defense of not wearing a shirt at a restaurant. Not everything is absolute - the degree matters. Having to wear a mask in public during a pandemic is a much lighter imposition of liberties than a habitual search of possessions and belongings, and arbitrary "random" strip-searches when one boards a flight.
The crucial difference is "the right to swing your arms ends at my nose" essentially. The actual impact on other people is what makes the limitations acceptable.
That is an important distinction compared to random searches because you "might" have done something wrong.
My thoughts are this: The statement sounds powerful and appealing. But if you think about what it means, really, it turns out to be an extremist viewpoint with little meaning. People who give up freedom for security don't "deserve" neither. We give up freedom for security all the time, and we are often better off for it. I would argue that without security you cannot have freedom; some security is necessary to achieve a free society. How free are you if you must constantly look over your shoulder to see if someone is coming to take what you have or hurt who you love?
So sure, we can talk about the trade offs and whether we should require IDs at the airport. But the quote, I think, is a misrepresentation of the stakes.