Nick Wilson has closely followed news on the war in Gaza since October. But Mr. Wilson, a Cornell student, is picky when it comes to his media diet: As a pro-Palestinian activist, he doesn’t trust major American outlets’ reporting on Israel’s campaign in Gaza.

Instead, he turns to publications less familiar to some American audiences, like the Arab news network Al Jazeera.

“Al Jazeera is the site that I go to to get an account of events that I think will be reliable,” he said.

Many…