“The question is whether the food is still pareve”? The bigger question seems to be whether those makpid on CY or permitted to consume DE or not.
I was also wondering if DE kosher certified commercial food has the same halachic implications as Cholov Yisroel food made in Cholov Stam keilim at home, for those makpid on eating CY. (Obviously in the latter case the food is milichigs.)