I'm squarely in group b, however, I don't think it's an actual dichotomy in the way you present it. I think American's fetishize "free speech" which leads to a "hyper group a" that argues since censorship is scary (which it is) we'd rather face any other conceivable consequence rather than wrestle with the hard questions of what is appropriate vs. inappropriate public speech. I believe we're seeing examples of where the pendulum has swung too far, in the US, towards "say what you want" and we need to bump it back a bit. If it swings too far the other way I'll quickly switch my thoughts on the matter.
Also, there's another dimension which I think gets immediately thrown on the floor when these discussions come up. Very rarely are people calling for controls on what can be said at any time. Instead, it's controls on what can be said to large amounts of people. Group b folks, such as myself, are not saying that we're concerned about dinner conversations. We're concerned about speech that is being amplified in a way where there's a civic responsibility to ensure that the harmful messages are not being amplified.