I think of those emoticons as innocent, if sometimes pretty goofy. First of all, there seem to be two distinct series, probably by different artists or even studios: what I call the "roundheads" like

and the "lumps" like

.
I tend to think of the "lumps" as haystack-shaped but on closer inspection they turn out to be triangles -- mostly with hair and/or hats that give them a rounder, more lumpish shape. Here's one undisguised:
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I imagine the person who drew them thinking how ridiculously easy they were to do: take the same basic character, put different headgear on them, and call them a cowgirl

, a bride,

, a viking

, or a Mexican :mexican:. For the cowboy

and the Catalan,

also leave off the hair.
By this reasoning, what would have led to the choice of a stereotypical Mexican was simply that the artist found it so easy to draw a recognizable sombrero.

It's not a statement about people of Mexican ancestry at all -- it's about the limitations of the artist and the format. (Are you listening, artist?

!)