They don't, typically. In rural areas some wear a pistol on their hips for snakes and varmints. Actual working ranchers often have something on them.
I don't know if that has ever actually happened other than people attacking cops. But they are generally attacking cops because they are cops, not for their gun. But yes, it tactically shows your hand and makes you a target.
Personally, I have mixed opinions. I get the point of both rights and the fact that your fear of a person with a gun or a sword or what ever is based on the fact that every movie and TV program shows people using them for crime, vs the overwhelming vast majority hurting no one with their weapons.
At the same time too many people doing that are also abrasive assholes about it, and it turns people off.
I like to make the point that I have a shirt that says, "Fuck you, you fucking fuck", and while it is my right of free speech to wear it, the appropriate places to wear it are severely limited and I would expect some squinty eyes.
But at the same time, you hear people calling cops on kids with Katana handled umbrellas and people in full STORMTROOPER costumes.