"Core values can’t be typed out or explained."
If you can't articulate them clearly, then you haven't thought about what they are to you. I'm not saying you have to have the same values I do, I'm just asking you to think about what yours are.
For instance, on the "left" a core value might be equality and equity. Leftists tend to believe that everyone should experience equal outcomes. You seem to believe this at least a bit, since you believe that Socialism is a desirable ideal (even if you don't beleive it would work for whatever reason).
On the other hand, I actually believe Socialism is a terrible thing, even as an ideal. Not even getting to whether it would work, I think its undesirable even as an idea.
So that might be an example of real tangible differences in values between us. That is going to manifest itself in our political positions. That is going to mean that you and I would prefer different candidates and parties. We might prefer different labels, etc.
But it is not just because we aren't looking at all the evidence, or being reasonable in how we think about something, or being emotional, etc.
It's because we actually have a different vision of how society should be organized.
So yes, it might mean we end up with different conclusions - such as whether we should have Universal Healthcare or not - but its pointless to argue about those things when we don't even share the same goals at the fundamental level.
So when we see 'democrats' and 'republicans' warring with each other, or the 'left' and the 'right' in constant conflict, there are sometimes very real and fundamental reasons that those groups disagree on everything that has nothing to do with political manipulation and everything to do with having different visions of society.