For a Christian, a top maxim in their value hierarchy would be rooted in Jesus' famous commandment: "Love the Lord your God with all your heart, soul, and mind." Now, if you're an atheist, this might be nonsense to you. You might not believe that Jesus was resurrected or that God even exists. To you, these are fundamentally irrational statements ("pigs can fly," etc.). Under your system, if you were an atheist and your opposition was a Christian, you could never possibly build a coalition because there's a disagreement at the top of the value hierarchy.
But this seems wrong because people of different creeds and value systems do stuff together all the time. Or am I misunderstanding your point? What I understand @Brendinooo to be saying is: "we may not share the same moral framework (or value hierarchy, using your term), but we do agree on X, so let's do X."
You are gravely misunderstanding my point.
You can hold some values as core to your position, your belief. Outside of your beliefs, there is a strict hierarchy of values.
Colors require perception, kinematics breaks down without velocity/acceleration.
Being Aetheist or Christian conveniently doesn't tend to conflict with the general hierarchy of values, which is independent of your particular religious interpretation of them. Your interpretation of the general hierarchy, can cause issues, however.
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.