I don't have any problemes so far when using the "Wave Texture" with a "Mirro Modifier" and a "Skin Modifier" on the snowman's arms in Blender 2.91:
Well that is good to hear! Perhaps it was something else in my project that was manifesting in a different way. If you can leave as many modifiers on your mesh, the more flexible it will be in the long run! -Chunck :)