intps can go quite deep down the rabbit hole with objective facts as well when arguing.
I dont think that you can define your whole type differently via that single thing.
I always have the impression that I am objective when arguing, but the problem is objectivism lies always in the eye of the beholder and doesnt really exist per se. I tho do know what you mean and how its frustrating for Ne users to talk to argue with Te users. Its not even so that we would want to argue but some Te users seem to always think it's there way or the highway and since that is so, arguing is inevitable. For an Ne user the independence of thought is more important and an arguement is thrilling because of how much abstract thought someone put into it and not because its an unbedanble fact (let alone the fact that all facts are bendable, even this one).
The distinction whether you are an entp or enfp is no easy one, tho there are people who may see that differently. For a primary Ne its not so easy and since we can imagine everything to be, its easy for us to tell ourselves something that might not be the objective truth.
I think if you dont go vertigo if you see glitter or unicorns its a good first indicator for your pness being ent