I think you confuse beliefs with values by placing that at the root.
I'd have a problem with it if my tax bracket were determined by whether I loved the Christian Lord rather than any other deity.
People of different faiths band together because of shared values that actually make a difference as long as they are happy to live and let live on matters of belief.
It is true that a lot of values sit on a foundation of beliefs, via the teachings we think are inextricably associated with our beliefs.
A Christian's values (e.g. "you are born a boy or a girl') might conflict with a trans person's beliefs ("I was not born with the body that matches my gender identity"). Meanwhile another Christian's values ("God has a plan and your body and gender identity must by definition be a part of that plan") might be entirely compatible.
Beliefs are absolutely foundational but all the values built on them are just received wisdom, interpretation etc.
Of course, it is easy to confuse these things, and people who rise to power are often those who do. Keeping an open mind requires time and mental energy. CEOs and world leaders rarely have time to examine their values, and refraining that act as "questioning my beliefs" reframes a rational act into an invitation to have a crippling crisis of faith - which is much easier to tell yourself is a temptation of the devil that you must not indulge.
By shying away from such examination they have much more time and mental energy and deciseness to execute effectively on their agenda.
The obvious downside is that this lack of reflection means the agenda they execute so effectively on is potentially not what they actually would have chosen if they'd really thought it through in a rational way.