I've lived in the US and in Europe and the UK. Shared culture is still very significant. If anything, maybe even closer now than in the 90s.
There's probably other reasons to think about the why and how of alliances than these.
I'm not a big fan of the UK, I grew up there and left. But this whole UK is authoritarian thing is totally overblown in the US media and HN comments. Having free speech restrictions implemented by an elected government isn't authoritarian. You could even say that having totally free speech imposed by a non-elected government is authoritarian if people don't want it. These things are separate. I listen to UK media quite often (topical comedies mostly) and my feeling is that these laws are generally supported. There's a lot of negativity about social media from bullying up to incitement of violence.
So is the EU, btw: Hungary, Turkey, and Israel.