Whether the wave function is real depends on your answer to the question: is momentum real? You can't directly measure or observe momentum, you can't point to it in the world, but you can definitely feel its impact and it's a convenient measure for certain properties of objects. In that sense the wave function is just as real.

But you can argue both those things are not as real as e.g. extension, force and energy, which are much more readily available to our senses.