What would be a good substitute for mushrooms in a Japanese udon noodle soup? Going more for a good texture. My partner hates mushrooms.

Go Ramen style and add some pickled vegetables. If you dine at Momofuku in NYC, you never know what type of seasonal pickle you'll find in your ramen, carrots, fennel, cucumber, turnip, the list goes on and on. The softer texture of the pickled items should give you the mouth feel you're looking for.

I had another thought. If you have access to mushroom soy (h-mart is where I get all of my Asian ingredients), it adds a huge amount of umami, but you can't pick out a mushroom flavor. Warning: it's very rich. A small amount goes a long way.

Nobody but knows the mushrooms are not there!
The udons I have are based on what is fresh and available.

Maybe this sounds crazy, but what about carrot slices? You could control the cooking so that they have the same bite as a mushroom, but of course they would add sweetness rather than umami.

Along the tofu train of thought, yuba (tofu skin) would be a decent textural sub for mushrooms. It's slightly chewy, though not as soft as mushrooms (i.e. shitakes).

Tempeh or firm tofu... gently crisp first by sauteing in a tiny bit of oil in a frying pan. You might want to add a small dash of fish sauce to the soup to compensate for the meatier mushroom flavor.

What about eggplant? I often add it to soups after roasting it quickly to get browned toasty edges.

I'm embarking on a 3 day ramen project this morning starting with making a shiitake dashi. :)