Another vote for unsweetened soy milk.

Unsweetened coconut milk--the kind in cartons, not cans.  Or unsweetened almond milk.

For mashed potatoes, though, I just skip the milk.

For mashed sweet potatoes, culinary/canned coconut milk is awesome.

For mashed potatoes, I mash them with chicken stock, EB margarine, Tofutti sour cream, salt, pepper, and chives.  None of the sweetness you'd get with soy milk.  Same general idea with chicken pot pie- I use chicken stock, extra margarine, and some extra flour for thickening. 

I've had the same trouble with soy milk in non-sweet foods.  I've had somewhat better luck with unsweetened (as opposed to plain) soy milk.  I've also drained (makes it less sour), and then whipped (using the stick blender) tofu and used it instead of soy milk.  The "soybean-y" taste usually comes through, however, and I have never figured out how to neutralize that.  Sometimes I just use chicken broth and "fake butter" for flavor instead. 

In terms of shared lines, I have found everything depends on the plant the soy milk was produced in.  One brand/product can be in multiple plants some of which are nut free and some are not. And whether or not the plant is "safe" changes constantly as nut milks are so popular right now. I just call the manufacturers directly and ask them specifically about the plant number to find out.  You can find the plant code stamped on top of the carton. 

We have been dealing with a dairy allergy for 10 years.  The kids drink soy milk and its great for baking but I find even plain soy milk has a sort of sweet taste in things like mashed potatoes.  Hedgie posted a recipe for me and I am wondering what milk alternative you use for savory dishes.  If you use soy and find it doesn't taste sweet, what brand do you use?