Relative to this historic norm, I don't think globalization and data hoovering is resulting in social cooling. The real issue is people are now being asked to conform not to the social norms of their parents that they were indoctrinated in from birth, but whatever becomes dominant in their online communities, and those norms may be less familiar and less stable, so conforming to them is less comfortable and more difficult.
You can sort of see this effect in the existing comments. "It used to be fine to say X, now you can't." We've always been conformists. That's how communities work. But people expect somewhat stable rules they can conform to. The unique aspect of the chilling effect we're seeing today is that people can believe they did something perfectly in line with norms, but then the norms change or they become part of a new community with different norms and some record of what they already did thinking it was okay is now no longer okay.
The thing that is unsettling to people is the rate of social change. It's not that they're being held to some standards of behavior. Everyone does that and everyone expects that. We never have been and never will be free to just ignore all laws and norms.