Since liquid water can't be compressed

Common misconception - it can, just not very much, so the volume change is tiny, and in practice, there's usually something else in the system that is changing volume by a larger amount- like air bubbles, or if there's anything elastic in the plumbing, it will stretch - but regardless, water absolutely can be under pressure.

resistance only reduces current, but when I think of hair in a pipe, the pressure after the obstruction would also be lower

You are correct, in electronics, resistance drops voltage (assuming the load is in series with the resistance). In fact, a cheap quick and dirty digital to analog converter uses a bunch of resistors to supply different voltages...