Joe is Jack and Ennis's boss on Brokeback Mountain. Like most of the other supporting characters, he seems to represent society's prejudice… in a very passive way.
He spots Jack and Ennis cavorting on the mountain: "They believed themselves invisible, not knowing Joe Aguirre had watched them through his 10x42 binoculars for ten minutes one day" (30). And while he doesn't say anything at the time, he clearly disapproves of what they do, which Jack learns when he comes back to see about more work: "Twist, you guys wasn't gettin paid to leave the dogs baby-sit the sheep while you stemmed the rose," and declined to rehire him (71). Joe has good reasons for it—the boys didn't do a very good job—but his tone suggests that he connects their poor performance to their homosexual relationship, which seems more than a little unfair.
Again, he never flat out cops to prejudice, but he makes his feelings clear. That kind of thinly veiled toxicity seems to plague Jack and Ennis a lot, and probably plays a huge role in making them so unhappy. Prejudice has a way of doing that.