When you see which, who, where, that and so on in a construction like this, you are dealing with a pronoun that stands for some noun, introducing a dependent clause. I suggest that if you have difficulty in analysing it, you separate the dependent clause, make a similar independent clause out of it, and understand what that is about before you put it back together. So, for example, here you might think about "Men and women are different from one another to some extent". To what extent? One which [again, a pronoun] people exaggerate.
No, you can't use "that" instead of "to which" here. You can sometimes use "that" as a stand-alone relative pronoun instead of "which" if it isn't separated from the noun it applies to, so I could actually have used it in the last sentence of the previous paragraph: "One that people exaggerate". But you need the preposition in your example, and so "that" is no longer an option (I know, it's a bit illogical, but that's the way it works).