I freeze soups such as homemade tomato-vegetable soup, lentil soup, beef-cabbage soup, etc. in those microwaveable plastic one-serving containers, and I haven't noticed any problems, not even with potatoes. I mean, potatoes and other vegetables in soups seem to be able the same texture they are in any canned soup, I guess, and much better than in store-bought frozen soups (such as Tabatchnik, which I think is vile).
Basically, I make the soup, mostly from scratch. Then I let the leftover amount cool to room temperature before putting it in the fridge or freezer. If you plan to freeze it, do so that day or the next. Don't let it sit in the fridge for days and then try to freeze it.
So... I don't know what problems the rest of you notice with freezing potatoes in soup or any other dish. I guess you could use canned Irish potatoes if that would work better.
I have a Middle Eastern dish I make that uses potatoes (and onions, spinach, cilantro, lentils, lemon, etc.) and I freeze that and it's fine, too.
This is all in an ordinary freezer, not a deep freeze.