I argued that since reality is entangled and our ideology has no consistent relationship with reality...

I think this statement is too strong. Our ideology doesn't have a 100% consistent relationship with reality, true, but that's not the same as 0%.

A good hypothetical example is a very good theory on the sociology of groups or ethics that makes usable testable predictions, perhaps providing a new perspective on politics, religion and ideology...

What, sort of like Hari Seldon's psychohistory ? Regardless of whether our society can absorb it or not, is such a thing even possible ? It may well be that group behavior is ultimately so chaotic that predicting it with that level of fidelity will always be computationally prohibitive (unless someone builds an Oracle AI, that is). I'm not claiming that this is the case (since I'm not a sociologist), but I do think you're setting the bar rather high.