As a very loose, general rule, filtered water won't have any "non-water" taste - it certainly shouldn't taste dirty (dirt particles would have pretty muh been filtered out.)

Will filtered water have a taste? Possibly; the filter won't take out all the chemical tastes (I've had water taste slightly iron-ish, for example, but not very often.

Remember, I hike in the eastern US (Ohio, Kentucky, Indiana, mostly.) I can't speak for areas other than that, since I don't have any experience.