The reality is that every source will have some sort of a view point which constitutes a bias. I think people should be careful with all sources, and it's actually good to look at viewpoints from across the spectrum. You don't have to agree with them or trust them, but it's often useful to understand their perspective even if for the purpose of framing a counterpoint. If you know a source like quillette has a particular bias, then you just keep it in mind when you read it.

The sources I dismiss are the ones that can't provide primary sources for the claims they make or are known to be factually wrong. These are the kinds of sources that constitute a waste of time and should be avoided.