Gun control, abortion, none of those are even remotely in the realm of 'core values'. They're just policy debates.
"My core values? MY CORE VALUES? You want to talk about MY core values? Oh buddy. I could go on ALL DAY about MY core VALUES! Don't even get me started. But I'm not gonna sit here and spell out my core values. No sir. Waste of time. They exist tho."
My core values would be that I believe that there are a set of natural, inalienable rights that all beings that qualify as persons possess. I would say that primary among these rights are the right to life, right to liberty and the right to property. I would say that there can be no just violation of these rights, under any circumstances.
Because I believe in these rights, I am obligated to denounce coercive acts as immoral. Even if I would personally prefer a practical outcome of some policy, if it violates my core beliefs I can't condone it.
What are your CORE beliefs? How do you come to your conclusions about whether gun control is a good thing or bad thing? What moral framework are you using?
You're stuck at the policy level, I'm asking about something more fundamental. You might say that your core values are loyalty, protection of family etc and all that would be closer to what I am saying, but since we are talking about the political realm I am trying to get at the core values that shape how you think politically.