This part is too broad.
Hierarchical values are just that. Not wholesale. We call that nonsense, e.g. I believe pigs can fly, therefore the sky is red. They are making an ontological error.
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."
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.
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.
By design. Activists and left-wingers in general enjoy losing and being underdogs and infighting constantly
It's per the usual for extremist ideologies, chock full of hypocrisy and nonsense.
Note that, I have no problem with conservative or liberal value systems...
But then you go on to describe exactly what @Brendinooo described, just under the guise of your system of "value hierarchy." The problem is that you can always default to "our values are hierarchically misaligned" and then never have to do any coalition building ever.
So how do you solve that? Because it seems that you can't.