Alternative explanation: The online world is "real" and the real-life interactions are "fake", at least as far as political opinions are concerned.
The social conventions for online and face-to-face interactions are still markedly different (with good reason). When face-to-face, we generally care a lot more about maintaining a pleasant conversational environment and usually avoid things that would insult or hurt the person we are talking with. The focus is also a lot more about everyday issues and a lot less about abstract political topics like it would be online.
All of this means that face-to-face, we will probably talk a lot less about divisive political topics than we would do online.
But it does not mean we have fewer opinions on those topics, only that we won't show them so easily.
So it could be that the online discourse really is a truthful mirror of the political division of society, only that in real life, those divisions are much more hidden behind layers of politeness.