Uhh, they have no contact with Gondor, or the North, they're blood sacrificers, not servants of the White Tree. They're enemies with Mordor, because Mordor is allies with the Morwaith, Half-Trolls, and Haradrim, who are all the Taurethrims enemies. The Taurethrim won't attack any one else, unless provoked, but they're only allies with Fangorn (Oddly).
Taurethrim are the ancient tribe of the jungles. They have a problem with morwaith for a VERY long time, and since morwaith is friends with mordor, half trolls, and harad too, Tauredain attacks them in return as well.
The ancient Taurethrim have some Mexica influences, but they are not supposed to represent an ancient Mexica-style empire. The Taurethrim of the later Third Age are culturally much more like the Morwaith.