Checking sources twice is something you should do from a news agency that is actually reputable. As in it trades on being honest and accurate.

You’re not obliged to read everything from an outlet that has no track record of honesty and integrity simply because you’ve been beaten around the head with the internet ‘logical fallacy’ meme one too many times.

Thinking that everything you read on the internet should be worth your time to fact check is the ultimate logical fallacy.

article titles on its Arabic website include "The Holocaust — that great deception", "Why do the Jews rejoice at the burning of Notre Dame in Paris?", "Jews and Freemasons in the Arabs' revolutions", and "The Jews of 'Israel'" — this is why their end is certain"

They also refer to the Ukrainian government as a "Nazi regime."

Your choice, but choosing to believe that site is plainly asking to be lied to. Advising others to "check sources twice" is pretty laughable in this context. This is unintelligent and blatant propaganda.

There is never going to be a case where the world misses the answer to the ultimate question of life, the universe, and everything because it was said by a Nazi and everyone refused to listen to the Nazi. When it's clearly straight up propaganda, it's perfectly rational to dismiss it due to the source and not investigate further. If there's a valid and useful point to be made, it'll get made in more respectable sources too and then it might be time to pay attention. Plus, even if they do cite sources, it's hard to spot where they've twisted or lied about those sources, but it's really easy for the propagandist to spout whatever nonsense they believe because they don't care about the truth. That asymmetry is good for the Nazi and bad for decent people, and the way to fix that is don't waste your time carefully investigating and critiquing Nazi bullshit.

Sorry, if you post Nazi propaganda and Holocaust denialism, you lose all credibility as a source.

Nazis are more than welcome to try to argue that they are a decent source, but anyone with a brain is going to discount the site and stories when you see the dreck they post.

“Journalists” who take money from these people don’t deserve that kind of respect. I’m not going to invest my time “checking sources” on propaganda, and expose myself to even more lies in the process.