(Noted not to dispute your point about civics education, but to stress this to other people who may not have been taught this.)
What about people in Nazi Germany hiding others? They were of course very secretive about it -- not being secretive certainly meant you and your charges being sent to a camp, and possibly outright death. Similar things happened with the underground railroad in the US. I would still gladly classify those people as civil disobedients.
Maybe there's a difference when you're protecting others? You can't risk being discovered, because then those who depend on you will also likely be discovered, and you won't be available to continue helping.
I think the difference is that if you are disobedient in the (current) USA then you will be dragged through an actual justice system and get the chance to make a case for future law changes etc.
People persecuted in Nazi Germany did not get the chance to argue their case in a court of law or public opinion. They just got taken away.
The martyr approach works well if your goal is to get society to recognize an issue and fix it. It's like an extreme form of demonstrations; the entire point is to be seen and generate discontent. This discontent becomes the energy that changes the status quo.
But if you're not capable of (or uninterested in) changing the status quo, but just want to "do the right thing", then evading detection is a much better approach.
Or you smuggle a persecuted across the US border it might still be illegal for you but you're breaking the law for a humanitarian reason. However, if you charge $5000 a person, any person from MS-13 to Isis to day laborers bring your toothbrush