Honestly, you seem to know a lot about math! 
I think the pushback has more to do with cultural differences than with actual disagreement over a “deterministic view.” In fact, I didn’t see much pushback specifically about consistency here — but I’ll make an effort to reread the thread.
P.S.
Consistency is also debated within the “causal” camp: Pearl disagrees with the potential-outcome framework. You might find this interesting:
https://escholarship.org/uc/item/6nv2744w