There is consensus that Media Bias/Fact Check is generally unreliable, as it is self-published. Editors have questioned the methodology of the site’s ratings.

https://en.m.wikipedia.org/wiki/Wikipedia:Reliable_sources/Perennial_sources

Even if you want to discredit those websites as a whole, it doesn’t change that those articles themselves are factual.

Mondoweiss is not a hate site. Anti-zionism is not Antisemitism.