At least from my part (and think some others also) the discussion is not really about realism but about the possibility of use a CIV5's Ideological Presure like system for others topics beyond contemporary socio-economic ideologies. The presented real world examples do not mean realism per se but the justification to abstract those others historical phenomena in a similar gamey way.
I may be one of the handful of people here who is a fan of Beyond Earth: Rising Tide, but that game (based on the Civ5 engine) took an interesting spin on "ideology."
First, the renaming... social policies became virtues, ideologies became affinities.
Like Civ5 social policies, virtues were earned using culture. Unlike Civ5, one could earn synergy bonuses by adopting them across categories and by going deeper within a category. Like Civ5, once a virtue was adopted it could not be "un-adopted" as the Civ4 civics could. Unlike Civ5, the pathway through the virtues had branches, both "and" and "or" conditions.
The affinities in BERT were mostly driven by tech/science, not culture. They were available throughout the game, not waiting until mid- to late-game as in Civ5. Affinities mostly served to buff your military units; each of the 3 affinities also enabled a victory condition if the player chose to go deep into that affinity.
Did the affinities set up blocs and potential end-game conflicts? Sort-of, and yes. I noticed a few AI (who were oriented to a different affinity) give me a diplomatic message, "Our cultures differ too greatly, this makes things difficult." It was still possible to trade with them and earn their respect.
As a player -- human or AI -- begins to fulfill the final conditions for an affinity victory, other players strongly object. This objection is nearly always followed by a declaration of war and invasion. My personal project is to win each affinity victory with each leader. Based on the data I've collected, the objectors are nearly always following a different affinity than I am.
Bottom Line: Yes, one could use a different concept to underpin the game mechanic and provide some more interesting game play in the late game.
It need not be tied to the word "ideology" nor the historical concept/definition of ideologies.