It appears that when playing with both mods, there is some conflict between the "Tail" slots created by each mod. Namely, if a mutant has WM's "Thick Tail" mutation, and adds a Stinger mutation using mutation points gained during gameplay, the Thick Tail gets unequipped and replaced with the stinger:
https://steamuserimages-a.akamaihd.net/ugc/1504719690102746971/84C39EB64190779031251E63A5774D66A70912EF/

Creating a character with both the Thick Tail and Stinger mutations results in a character with the Thick Tail mutation, but without the Stinger.

There also seems to be some kind of wonkiness going on with the Fluffy Tail mutation playing with both mods - when I took it I didn't have the tail show up on my equipment screen at all, which I'm assuming it's supposed to? It did add an extra tail slot, it just didn't put anything in it. Don't have a screenshot of that, as I didn't think to take one, though.

Not sure how hard it would be to make the two mods work together (I'm guessing it's a matter of both mods using the same identifier for the "Tail" slot or something similar), but you both have really solid mutation mods and I'd hate to lose out on one or the other.