Both are not correct.
Some of the ideas that were in the fringe of left (like racial justice etc) are more mainstream now. Both liberals and conservatives have moved to the left on those issues.
- There are still a lot of conservatives who haven't moved or have moved slower than the median person. They think the world is falling apart (or that they have been left behind)
- There is a reactionary right ("alt-right") that wants to push back very hard on the cultural issues and indeed want to go back to pre-civil rights days. Infact an exit poll during '16 primary found 1 in 5 Trump supporters opposed emaciation proclamation
- A progressives have pressed for many left leaning economic ideas for sometime now but have gone nowhere. Including ideas like single payer healthcare that is what ALL the other industrialized countries have. Many on the right claim single payer is "socialist" / "commie".
You have to really go issue by issue. I think we agree but are just saying it differently, for example, when you said:
"There are still a lot of conservatives who haven't moved or have moved slower than the median person.
They think the world is falling apart (or that they have been left behind)" (emphasis added)
Look if you would rather have LGBTQ people stay in the closet, or sort of liked a "don't ask don't tell" policy, my point was society at large has agreed with the left's long standing position that merely tolerating such people is not enough, you need the first openly gay general or whatever.
Now, what I often tell my liberal friends is that I see no logical reason to assume anyone would be evolving or changing their mind on one or more of these social issues. So, I would say, not only would such a person "think" their world is falling apart IT IS FALLING APART.
If you never imagined having to even discuss gay marriage, and the next thing you know you are a baker and you have to make a gay wedding cake, look YOUR WORLD IS FALLING APART.
So I see what many here have labeled as conservatives "moving right" is sort of the natural reaction of the side where their view on a particular issue now seems to be in the dustbin of history.
As for Twitter, this boils down to what appears to be not just free speech, but the continued right to offensive speech, or, to put it another way "allowing the speaker to determine whether or not something is offensive." On super free speech Twitter, the Washington Redskins are still the Washington Redskins, for example, and there is no fallout from making such a reference.
I mean, in a way this is the only forum where you can have these discussions logically, but I never imagined I would be having them with respect to Musk buying Twitter. Sheesh.