I struggle with this. Where I live, it's harder nowadays to compartmentalize how someone votes from their core values. What we used to call "politics" now encompasses some fundamental aspects of how we observe and process our daily lives.
This would then let you see your neighbors as people. What you claim are core values are nothing of the sort. They are misconceptions invented by your in-group to dehumanize the out-group. In reality people's core values are: their kids, their health, love, belonging, a sense of purpose. The rest is just a puppet master hijacking these core values for organizing a crowd.
Core values are about how you treat people who are NOT close to you, how you believe limited resources should be allocated, how and by whom you think decisions should be made, what the relationship between individuals and society ought to be, and specifically between individuals and government.
You say "values like how you treat people who are NOT close to you". Which is really code for "people who like open immigration policies are virtuous and people who oppose them are bad and/or less intelligent". But once you drill down to details - the picture changes. This kind of sentiment is used to drum up support for very specific pieces of very questionable legislation. Why should a specific ethnic group with a large and powerful diaspora get a free pass to ignore immigration laws, but other ethnic groups get the book? How is this about being virtuous and treating people NOT close to you equally? Well, you aren't allowed to ask these questions - you don't want to be a part of the dumb racist outgroup, do you?
If your core values are the there should no border controls at all, those are your core values. If your core values are that we should very tightly controlled borders, those are your core values. If your core values are that we should let in more Norwegians and less Bangladeshis, or vice versa, then those are your core values.
My point wasn't that a particular set of core values are virtuous, it was that core values are not things like "loving my kids".
By that definition maybe even "loving my kids" wouldn't pass the test, as Viktor Frankl explains better than anyone could.
As for immigration, it is no accident that anti-immigrant rhetoric is on the rise precisely when the economy is doing poorly. When there were enough resources to go around - there wasn't nearly as much reason to oppose immigration. Which means that "my family is financially secure" is a much more core value for most people than being open to the world (even if they'll never admit it).
That's less true IRL if you just talk to people and be personable. There's something about seeing someone face to face and chatting that helps you intuitively understand you have a lot in common with them (or not) - and regardless of their political opinions either way.
I find that the sorts of life choices people make and the character they have as a result is a far better discriminator of what they actually have in common (or don't) with others.
I think that's even true when a horrible ideology is gripping a nation. The Bolsheviks and Red Guards were not to be reasoned with by neighbors in their heyday. "The wise man sees trouble coming and hides himself."
"He who turns a sinner from the error of his way will save a soul from death and cover a multitude of sins" (James)