Each of those beliefs individually can be true or false (or disconnected from evidence). These beliefs should be debated individually.

I don't think it's quite that simple.

You are arguing for atomicity of beliefs as well as their independence -- you are saying they can (and should) stand and fall on their own. I think the situation is more complicated -- the beliefs form a network and accepting or rejecting a particular node sends ripples through the whole network.

Beliefs can support and reinforce each other, they can depend on one another. Some foundational beliefs are so important to the whole network that rejecting them collapses the whole thing. Consider e.g. Christianity -- a particular network of beliefs. Some can stand or fall on their own -- the proliferation of varieties of Christianity attests to that -- but some beliefs support large sub-networks and if you tear them down, the rest falls, too. At the root, if you reject the belief in God, debating, for example, the existence of purgatory is silly.

The package-deal fallacy exists and is real, but excessive reductionism is a fallacy, too, and just as real.

If we collectively fail at rationality 101, I don't trust our ability to debate more complex things.

Oh, I don't trust our ability to debate complex things. But debate them we must, because the alternative is much worse. That ability is not a binary flag, by the way.

There is more than the value; there is also the model of the world

True, and these should be separated to the extent possible.

It seems to me that people usually differ more in their models than in their values.

I don't know about that -- I'd like to see more evidence. One of the problems is that people may seem to have the same values at the level of costless declarations (everyone is for motherhood and apple pie), but once the same people are forced to make costly trade-offs between things important to them, the real values come out and I am not sure that they would be as similar as they looked before.