No, not really; the problem is more, taking things that were originally introduced with the intention of being abstract pictograms signifying emotions; and adding enough un-called-for detail (i.e. details not required by the Unicode codepoint description) as to make things like gender and race seem like a relevant or even necessary property.
Consider: in all modern implementations, "emotion" emoji are displayed with... heads. Opaque backing "vaguely skin-tinted" blobs at the very least; full-on human heads with ears and noses and hair in some fonts.
They don't need to be. Nothing about the Unicode codepoint for e.g. U+1F603 "grinning face with big eyes" says the "face" needs to even be visualized as being on a head. It could be doing a cheshire-cat-smile thing, just eyes and a mouth — ":D" but rotated 90 degrees. And, in fact, that's exactly what it was, in the DoCoMo image-font, one of the three that led to the Unicode introduction of emoji!
But for some reason, now we don't just have skeuomorphism (shiny eyes, pink mouths with tongues, blushing cheeks); we have these heads, and ears, and hair; and before you know it, people wondering why the head is yellow rather than some actual skin tone; or why the increasingly-less-generic face shape seems to be more masculine than feminine; etc.
Why not just cut the Gordian knot? Get rid of the "head" part. Get rid of any part that's not required to communicate the concept. Make an image-font of only the Minimum Viable Pictograms for what each of the Unicode codepoint descriptions describes.
Which is orthogonal to skeuomorphism, mind you. This isn't about whether a tongue has a tongue-ish texture to it. It's about whether you should include a tongue at all.