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Snopes is well known for its fact checking honesty. I have found them to be highly accurate. They will deal in more mundane things than just the big picture lies of Donald Trump. They certainly have been accused of favoring liberals, but any website that reports facts will catch the ire of Republicans, especially the Trumpians. I judge them by their content and not attacks on their character. I have compared their responses to those of the Washington Post Fact Check, FactCheck.org and Politfact. Without question, Snopes holds their own. I trust them.
Consider that "Trump as of Dec. 10 had told 15,413 untruths during his presidency, The Washington Post’s Fact Checker column reported. Many of them earn four Pinocchios.
Likewise, FactCheck.org lists countless lies, big and small. For just 2019 here are a list of his biggest whoppers.
Politifact also keeps track of Trump's lies.
But if you want a comprehensive list of Trump lies, rants and other dubious things Trump says or does, go to Inferior Donald.
There are no fact checking websites with a strictly liberal or conservative bent that I can see. Fact checking is done by all these groups, and a fact is a fact. There are no "liberal facts" or "conservative facts". The "alternative facts" of Kellyanne Conway are not facts...just made up bullshit to placate the president's moods.
I might disagree with the "false" versus "mostly false" ratings of the fact checking organizations, but the descriptions of these organizations are generally factual...right on...the truth. I will acknowledge that Republicans living in an "alternative reality show" are incapable of recognizing the truth. They hide from it. They fear it.