Pillagers have no hood texture, unlike other illagers.
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With MC-116911 being resolved as WF, I'd suggest to turn this report into the opposite as it currently is: witch, vindicator and evoker having one being the issue instead (as the hoods are deliberately not in the model rendering, them being in the texture should be a valid issue)
I'm pretty sure that the bug here is that evokers and vindicators have a hood texture in the first place.