Lot of left leaning groups do not openly advertise as left leaning

I am finding a peculiar trait common to all regions.

If a group is left leaning or woke, they advertise themselves as centrist, or Majoritarian. They do not openly call themselves led or woke. Eg r/politics etc (there are many groups like this)

But right leaning group, openly admin and call themselves right leaning. And they allow left leaning people to participate in their discourse too.

Very strangely, I am finding right leaning people open to ideas and discussions. While left leaning groups cancel any one who speaks against their popular discourse.

Till recently, I was under the opinion that Left leaning are open minded and conservatives are closed group, but its the other way around.

This is not just for USA, it's for all around the world. Left leaning practise more censorship, become authoritarian, and are mostly self inflicting (like opening borders and inviting criminals in) except for the Chinese.

Is my observation right.