First off, with all types of cleaners, make sure to test a small inconspicuous area before proceeding to do the whole thing. This will save you a huge headache down the road if the product has a weird reaction to the material that is being cleaned.
Having said that, yes, we've already had a few customers use this on their headliner with great success! This product should be safe to use on every surface except for glass and delicate instrument panel screens such as your speedometer cluster and navigation screens.