This is empirically not true, especially if you look at the policies of and donations by Google, Twitter, and Facebook.
Google donates to both parties; Twitter obviously has a very laissez-faire to the Right's voices, including the POTUS, and its COO recently suggested that if Trump canceled briefings, he could take questions directly on Twitter. And the evidence and rumors continue to swirl about how multiple Republican Party candidates campaigns used Facebook's own incredibly specific ad targeting, which they did not revise until after the election. (cf. Cambridge Analytica, contracted by Cruz and then Trump to "manage" the election outcome.)
[1] http://thehill.com/blogs/pundits-blog/media/303295-how-faceb...
[2] http://gizmodo.com/former-facebook-workers-we-routinely-supp...
I'm curious, what in your opinion are some "right leaning" fact checkers or "agnotistic" fact checkers?
We're all human and we have our biases, whether we like it or not. It doesn't take much effort to tweak an assertion to go from "Mostly false" to "mostly true" - it just depends on which one the writer favors. My BS detector goes haywire whenever someone claims to offer non-subjective anything. tl;dr investigate facts and claims yourself and never trust those who have power over you, even if you vote for them!
Also, what are some "right-leaning" fact checkers then?
Twitter isn't laissez-faire with right leaning voices. They actively suppress them. They remove hashtags from trending daily. They mark posts as containing explicit content. It's getting ridiculous how much all of these companies are trying to silence the right.
Facebook will take almost anyone's money on their ads. But they were also caught this last election cycle actively suppressing conservatives. It got so bad Zuckerberg had to come out and do damage control by inviting conservative commentators to a sit-down or piss off half his US userbase.