Jeff, you're a tough poster! You won't let anything slip past unchallenged. I'll have to admit I got the idea from somebody else here (I hate not being able to credit the right person, but worse to credit the wrong person, who might not even agree -- for what it's worth, it was a man). Anyway, the interpretation made so much sense that I adopted it as my own.
Here's the idea: Ennis is essentially presenting himself to Jack's parents as Jack's boyfriend. ("I'm the queer who loved your son," is how the other poster put it.) True, he doesn't come right out and say so, but both parents in fact do realize it, and it's not farfetched to think that Ennis anticipated that they might "suspect." Disposing of someone's ashes is a pretty big deal, disposing them on ground that Ennis and Jack had occupied together 20 years earlier is suggestive. Lureen got it, and in that light I think her suggestion was kind. (More motivated by wanting to offer Ennis some slight consolation than because she was concerned that Jack's wishes be carried out. Bout the ashes, I mean.) Yes, Ennis can pretend they was just good friends, but the nature of their relationship is such a subtext of the whole scene ("Tell you what, I know where Brokeback Mountain is" -- i.e., "I know Jack was gay") that I think we have to credit Ennis with recognizing and even expecting it.
It appears to me, from the way Mrs. Twist steps onto the porch with coffee already brewed, that they knew he was coming. Why the disposition of the ashes wasn't already discussed, I don't know. Maybe he just sent a card. Maybe he talked to Mrs. Twist and she didn't discourage him from coming. We're probably not meant to investigate that question closely.
The point is, going there in the first place was an uncharacteristically bold move on Ennis' part. It's the first time he has acknowledged, however implicitly, the nature of his relationship with Jack to others. He's pretty openly (albeit subtly) emotional -- with Mrs. Twist, anyway. There is eye contact between them, even before the shirts, suggesting that she gets it and that he knows she gets it. He doesn't appear to worry much about that.
So all of these things suggest that he has accepted his sexuality by then, or at least reached a heretofore unknown level of acceptance. My interpretation of the closet scene is that it has more to do a realization about love, rather than sexuality.