Liberals are generally not considered left wingers.
Much of the world generally considers "liberals" to be center right.
Many conservatives literally feel they are doing God's work, or that their views are justified by God, which is literally as self-righteous as it is possible to be.
Most people think they're morally justified. But they're not advocating for policies or taking action to damage conservatives.
There's a huge difference between thinking someone is better than someone else, and actively advocating for policies that hurt that other person.
Florida Republican pitches bill to ban the state Democratic Party
In politics, the word left is applied to people and groups that have liberal views. https://www.dictionary.com/e/leftright/
So, yeah, I'm gonna go with that.
Using US terms in a thread labeled "US Politics" aside, the sophistry, self-righteousness, and hypocrisy baked into your post is exactly what I mean. You're actually trying to downplay bias and prejudice, which is kind of amazing. Interesting that you don't deny it, though, and instead go with the Whataboutism option.
Democrats are just as much about devaluing certain categories of people as conservatives are. They don't try to understand, they simply condescend. It's the party of arrogance and telling people what to think. It's the new Moral Majority.