I'm not sure how important they are.
In the short term, they're not important at all. However over the life of the car, those plastic inner fender liners make a world of difference. I've worked a lot on the 80's chrysler FWD's, and they came from the factory with front fender liners only. Here in Manitoba, it's hard on cars rust-wise, and the front fenders are always in great shape(even if the floors are rotted out) and the rears are the ones that are more prone to rusting out. And fender lip can be a very bitchy area to fix. I've repaired the rust on a couple, and depending on the shape of that area, that can be a real bad spot to fix. Civics are very flat in that area, so they wouldn't be as bad to repair, but still, prevention is the best bet.