Here's a few links on their anti-conservative bias:
- They work with the far-left hate-group called SPLC and use that highly biased source to flag what is FakeNews or not. I guess ThinkProgress and HillaryForPresident.org was too busy and unbiased for them.
- Facebook's political contributions (by party) is about 2:1 for Democrats (even when Republicans are running things), that's better than the 100:0% split for the first few years. 
- 2019.02.27 - whistleblowers released internal documents that shows exactly how FB has been intentionally suppressing conservatives. But trigger word ranking and "deboosting" (de-ranking). 
- 2018.08.29 - Sunnyvale Dept of Public Safety (and some other counties) are teaming up to make taxpayers overpay for guns, in a misguided "gun buyback". The idiots promoted it on their Facebook page. Since that violates the rules of Facebook (to buy/sell guns using Facebook), a bunch of folks Reported it to Facebook as a violation of their terms. But since Facebook's first rule is to break the rules for issues they care about, they of course did not fix their rules, or throw the offenders off. Proving their hypocrisy.
- 2018.08.21 - I got a post flagged, and restored for Hate speech - silly, you'd have to be an idiot to report it as hate speech, and a bigger idiot to fail to recognize that it most definitely was not. But alas, in the world of perpetually butt-hurt, anything you say (including leave each other alone) is likely to be seen as a hate crime.
- 2018.06.21 - Bans an ad for a movie (Trump Prophecies), because it has Trump in the name. 
- 2018.04.02 - Bans image of Jesus on the cross 
- 2018.03.19 - According to Edward Snowden, Facebook is just a surveillance company branded as "Social Media" 
- 2018.03.14 - FB Bans Britain First for being anti-immigration or "right wing". They claim for violating vague speech codes, but they do not lay out a case for it (other than Trump retweeted videos that seem to accurately claim that Muslim mob threw a kid off the roof and beat him, or stuff that the left claims is hate speech to expose). If they showed objective standards, and how the terms were violated, I might be sympathetic. (Or if they were banning those that retweeted CNN videos that were inflammatory against the right or gun owners), then maybe they'd have a moral position. But inferring that anti-immigration is the same as hate speech (while ignoring hate speech against conservatives/gun owners), and not being able to back it up with details, is just incompetence/bias, masquerading as snowflakes version of tolerance. 
- 2017.08.10 blocked Trump supporters Diamond and Silk‘s page with 1.5 million Facebook followers after determining their content and brand were “unsafe to the community." The block only lasted 8 hours until it was appealed/reviewed, but the point is this never happens to left-of-center sites. 
- 2016.05 - There are multiple employees that admit they "routinely suppress conservative views"  including the following next events had been secretly downgraded:
- blocked stories about CPAC
- blocked stories about Mitt Romney
- blocked the posts of a FOXNews reporter
- blocked over two dozen Catholic pages
- blocked stories about the Lois Lerner IRS scandal
- blocked stories about Glenn Beck
- 2016.02 - Anti-diversity memo - Few Owner/Managers can drive a culture where diversity of thought is truly welcomed (egos often favor yes men). Facebook and Mark Zuckerberg not only didn't break that trend, they were famous for demanding sheep, and became more so when Zuck sent a Facebook-All email/memo in response to "All Lives Matter" chalkboard art, that "no" they don't. Some lives matter more than others. Message received, there can be only two sort of thinkers at Facebook: (1) far left dogma regurgitating far-lefties, or (2) silenced conservatives that know how to nod and pretend to be the former (3) unemployed free thinkers, conservatives, libertarians, or anyone that isn't in group 1 or 2, and doesn't know how to remain silent. 
- 2016.01 - Israel Project did an experiment where they showed equally offensive anti-Israel and anti-Palestine videos, and of course the anti-Palestine one was taken down. Only after it caused a stink, did Facebook take down the anti-Israel one. Now no one would confuse something called Israel Project with an unbiased source. But their evidence was pretty obvious. They later pulled the story and examples. No one is sure why, but FB demonetizing or deleting conservative pages they don't like is a pretty strong hint. Whether that was through direct threats, or just Israel Project seeing the writing on the walls, doesn't change the point. 
- 2014.02 - If you want to see if they're stupid-left, to what absurd degrees they'll go to appease the intersectional marxist, you need look no further than their 57 genders -- which confuse sexual preference with gender . Physical gender isn't that hard. Male (XY), Female (XX), Both (XXY, XYY). Done. The rest is sexual preference. While I think people's uniqueness should be respected, FB proved they're close-minded by only using the sexual preferences as seen by SF/Seattle LBGT communities instead of being fully inclusive and adding in: experimenting, drunken mistake, glory-holer, Frotteurist, Pederast, Objektophilie, Necrophiliac, Coprophagiac, Beastiality (each animal or group should be called out), Celibate, Banjee, Voyeur, Exhibitionist, autoerotic asphyxiation, crush videos, and so on. The point is, I don't care. You can do whatever you want to among consenting adults, but your kink isn't your gender. And if you're dumb enough to think it is, then list all possibilities, instead of the politically correct subset and pretend that's tolerance.
- 2012 - Facebook actively worked to help get Obama elected/re-elected and give them more data than anyone else. This raises issues with unfair practices, and the value of the support they offered (and campaign finance law). It certainly shows evidence of collusion to subvert an election.  Carol Davidson (head of Obama's re-election media analytics team) said at the time, "Facebook was very candid that they allowed us to do things they wouldn’t have allowed someone else to do because they were on our side."... to this day, Zuckerberg refused to admit any political bias or that he’s been suppressing conservative speech (despite evidence of both). He lies every time he claims they are evenhanded.
- 2012.07 - shut down the Chick-fil-A appreciation day page (later restored, after damage done)
The point is that Facebook and Zuckerberg pull out the excuse, "just a bug with our algorithms", "automation bug", or something like that. But the facts are that while Zuckerberg was prepared for the question (as he's been getting it for 5+ years), he was unable to point to a single Liberal candidate or notable left-wing poster that was blocked or saw a drop in traffic. That means either they're idiots who can't code, or their assumptions aren't valid in writing the "algorithms". In other words, they trust hard-left places like ThinkProgress, SPLC or PolitiFact as vetting truth, when all they really show is proof of bias.