How would you as an individual deal with having inconsistent values? Let's assume that you become super intelligent, so you can rather reliably see the possible consequences of any changes you would try to do.

The person who takes their religion very seriously probably believes that the religion is factually true. Or possibly they believe that the religion is false, but that it is a "Noble Lie", i.e. that the belief in the religion is a net benefit. Either way, there is an empirical claim they have related to the religion. They would probably be interested in knowing whether this claim is true.

These are not full answers, just hints towards possible answers.