Absolutely. Take religion for an example. There is no factual basis for any religous claims made and yet millions of people believe in their religion of choice. Even the Darwin theory is not factually based. It's a theory. But yet many people believe it. The Big Bang theory is also that.
Everyone has the right to believe whatever they want to, and everyone should equally respect the right of others to believe what they want.
The best option for me is to view ALL sides with an open mind, and be willing to concede, if true facts are presented, that my beliefs could be wrong.