It is surely incumbent upon us all to be intellectually honest about the things we believe in – even if it is only to ourselves. Even our most centrally held beliefs must be available for inspection, and subject to alteration if for instance new evidence surfaces that makes the belief no longer tenable.
For instance, an intellectually honest theist must be able to say something like ‘I believe in God, but if xxx should happen, or evidence for yyy should be presented then I may have to alter that belief.’
As a (hopefully) intellectually honest atheist I deny the existence of any gods. I would however have to seriously consider that position if for instance a DNA sequence present in all life was found to decode as ‘© 6000BC God’. Or if a god appeared undeniably before me and a (statistically) large crowd and was able to uncontestably demonstrate their divinity.