Ah I had forgotten about the term "hegemony", thanks for reminding me! I will use "hegemony" in the future instead of "base culture". At a surface level it seems to be a term that accurately conveys what I meant by "base culture", but will have much wider recognition than some term I invented.
And rereading your original comment in the context of this comment, I think I understand your point better. When one uses the term "judeo-christian culture" they imply multiple things, some of which are incorrect:
1. That the collective systems of the US operated under a single shared system of beliefs. I would have referred to that as "culture", but perhaps the better term is "hegemony".
2. That most individuals in the collective "liked", or rather "personally subscribed", or rather had a culture compatible with that single hegemony.
You are arguing that point 2 is incorrect. There have always been many cultures present in the US, but due to Judeo-Christian hegemony, those other cultures expression was suppressed and the "Judeo-Christian" hegemony was all that presented. Users of the term "Judeo-Christian culture" are not recognizing that many members of the "Judeo-Christian" hegemony were only participating in the hegemony because they _had to_, not because they _wanted to_.
On your other point:
> Article author and grandparent are conflating political participation/power with demographics and trying to map complex multi-dimensional political realities onto a two-dimensional liberal/conservative lime
I think you are mostly right about this; however I think that within the right wing, demographics, culture, and politics are largely intertwined. I think those demographics, culture, and politics are largely the ones that were traditionally present under Judeo-christian hegemony.
So, refactoring my points under my new understanding, I think:
1. We both agree that the US had a Judeo-christian hegemony (perhaps there is a better name needed).
2. We both agree that the right wing is descended from that Judeo-christian hegemony.
3. We disagree to the degree that various Americans' cultures across history were compatible with the hegemony or were suppressed by the hegemony.
4. We likely disagree on whether a [edit: replaced "the" with "a" here] hegemony is good or bad.
On 4), I get the sense that argument will be rather boring. On 3), I would love to get some references to material that studies this. I do not particularly care if the material has a left or right bias, as learning those perspectives would be interesting itself.