Joe Aguirre is a homophobic tightwad who owns a ton of sheep that graze every summer on Brokeback Mountain. And he plays double duty: Aguirre is both Jack and Ennis's employer, and he's a father figure of sorts. He's distant, disapproving, and homophobic, just like Jack and Ennis's real dads.
After watching Jack and Ennis wrestle he brings them down from the mountain, almost as if he's attempting to split them up…even though their relationship doesn't affect Aguirre in any way whatsoever. However, Aguirre is the type of man who's threatened by the mere existence of homosexuals. He later refuses to re-hire Jack because he is gay.
Yeah. This guy's the worst.
We never see Aguirre after this. But it is Aguirre's refusal to rehire Jack that sends Jack back to the rodeo in Texas, where he meets Lureen. So although Aguirre is a total jerk and we want to punch sofa pillows every time his smirking mug appears onscreen, he does contribute the film's plot. We'll give him that much.