"Everyone is entitled to his own opinion but not his own facts". Political parties/religions are based on "their own facts". Aren't they?

Former US Senator Daniel Patrick Moynihan said that. Sounds great doesn't it? Not practical.  If everyone used the same facts there would be no division of ideology. How could there be?  But politics and religion are all about division so clearly the facts they use differ.  Which fact is most factual? Depends upon the beholder's eye. Doesn't it?