Sources with direct knowledge tell us ... every member in the Hadid household -- including Gigi, Bella, Anwar and even their parents, Mohamed and Yolanda -- have gotten ominous messages that have made them fear for their lives.

We're told these death threats are coming through multiple mediums ... including emails, social media and even their own cell phones.

Our sources tell us phone numbers of several Hadid family members have been leaked online over the past week -- in other words, they've been doxxed -- and they've had random people hitting them up with horrific sentiments ... including graphic descriptions of how they would carry out the Hadids' executions.

It's forced the hand of the Hadids, whom we're told have all had to change numbers to avoid the ongoing threats. It's gotten so bad, our sources say Mohamed -- the patriarch -- is considering going to the FBI.

Gigi broke her silence in the wake of the Hamas attack -- which came across as measured and nuanced, but her latest remarks have drawn the ire of Israel itself.

That disgust appears to have manifested into blind hatred ... and it's having real-world effects on the family.

Other members of the family have yet to address the Israel-Palestine issue publicly.