"However, there is nothing wrong with having core principles that aren’t able to be swayed"
That's called being dogmatic. Sure, extraordinary claims require extraordinary evidence, but, in the face of extraordinary evidence you'd be a fool to stay unswayed and adhere to your proven false core principles.
I would venture to say that not all dogma is misplaced, despite the negative feelings that word tends to ignite. I tend to use that word more in situations where it’s clear someone hasn’t reasoned out why they believe what they believe. When I use the word “principles” I think it different than someone who just follows rules they were told to follow.