The bias and censorship on HN is a perception, and a perception which happens to be accurate. I would love to “prove it with data” but I have more productive uses for my time than painstakingly collecting information on the disastrous stewardship of an aging internet forum. I am doubtful that many could be convinced of these things anyway, regardless of compelling data or stirring rhetoric. That being said, the clear moderation biases on HN have been noted on certain stories by many people which are often conveniently flagged and memory holed. You pick and choose, or perhaps you allow the flag brigades to pick and choose which stories stay up and get taken down. A great example in recent memory was the James Damore Google memo controversy. Numerous articles and blog posts with hundreds of points and comments were flagged to hell until suddenly a story with the correct narrative floated to the top of HN and stayed there for hours.
Maybe that was the moderation team, or maybe it was the community. Either way, to claim that that episode was given a fair and even handed treatment on this site is complete BS. And there are many other similar examples over the years.
The truth is that these narratives are all made up, based on however what people notice passes through whatever filters they have. That's also why these digressions are so tedious—they're self-referential projections.