The five liberties enshrined in the First Amendment have seen better days -- in terms of public support. The Newseum Institute reports that there are some demographics that don't even have a majority in support of basic freedoms like freedom of religion.
I don't think that's the kind of thing we can solve in schools (though civics education plays a part). It's the kind of thing that starts at home.
The First Amendment freedoms aren't any good if we're selective about them
The core values of a free society under the rule of law don't just spontaneously regenerate themselves. We have to celebrate and amplify them. But it also means we need to call out our fellow Americans when they cut corners on personal liberties.
A well-meaning individual replied to a Facebook thread about this very subject (in which I was involved). Their response was to blame the schools for a shortage in civics knowledge: "If our K-12 education system was doing what it should be doing..."
Respectfully, I would submit that the problem begins at home. If parents aren't imprinting civic values before kindergarten and reinforcing them every day after, then it's asking a lot of any educational system to do the work of producing worthy citizens.
"School is an invaluable adjunct to the home, but it is a wretched substitute for it." - Theodore Roosevelt
If we all spent less time thinking that issues like civics were someone else's problem (and complaining about other people's bad parenting), then we'd naturally create the kind of peer pressure that would make people want to conform.
Sometimes it takes someone who wasn't born into those freedoms to really appreciate them: