According to some propaganda I recently read--and that's a lot more likely to be representative of modern Christian thought, it being what they themselves use to try to rope more people in and all--the sin isn't the same "original sin" stuff that, y'know, is called "original sin". It's a vague, un-detailed sinfulness the origin and nature of which remains ever distant in their explanations. It's just some vague thing like "Man is sinful by nature. Only by accepting Christ can you achieve salvation." Basically, they think of sin like sweat or dead skin cells--your body (or soul, I guess, in this case) just naturally produces it--and they try to sell Jesus et al. as a sort of spiritual shower.
There are entire swaths of Christianity that affirm that a believer only needs--at most--half (the second half) of Bible to "be a christian"--no Adam-and-Eve-originated original sin needed. I agree, naturally, that this explanation is batshit crazy, but, hell, so is the one with "original sin" in it.
The problem is only between dogmatic christians and evolution. The consistently-made objection to evolution by creationists is that it stands in opposition to their sacred scriptures. They see it as being part of a super-global (usually Satan-originated) conspiracy to just be a dick to god by disagreeing with His WordTM.