It's not right-wing as much as a particular kind of very free-market-focused libertarianism. But, yes, I've thought about this discrepancy, too.

In practice, big services like YouTube, Twitter, Reddit, et. al., are going to get heat from all sides of the political spectrum. Right-wingers are positive Twitter is suppressing them, yet left-wingers frequently complain Jack Dorsey is a cryptofascist. Both of them are pushing these theories on... Twitter. And they get thousands of retweets. You would think that irony would not be lost on them, but you would be oh so wrong.