Hello lance!
I know that this is an old discussion between the two of us. 
But "love" itelf is a label. It matters that we call it "love", and not "sin" or "lust", as others would call it. The phenomenon is the same, but see how much of a difference the viewpoint makes.
It's not my position to insist whether or not "gay" is appropriate for Ennis or not. But I would say that it does matter.
"Labels" do matter very much. I don't think we can and I don't think we should be free of labels.
Hey, bud. It's good to re-visit old discussion once in a while to see if we can achieve a new level of understanding.
Love is indeed itself a label. And as we agreed in the past, labels are indeed important as means to communicate. However, it is also important to remember, as is said in Taoist philosophy, "the Tao that can be named is not the Tao", or as Immanuel Kant put it, "the noumenon is not the same as the phenomenon". As long as we remember that the label is not the same as the thing, then we will continue to search for the thing, not thinking self-righteously that we have THE answer. This last point is what I mean when I say that we need to be free of labels, to be free of our own prejudices that arise from labels, like stereotypes, caricatures, demonizing the others.
What you said about love, lust, sin etc, is a perfect illustration of the trappings of using labels and mistaking the three different levels:
1. noumenon (the object thing which is independent of the universe, the unknowable essense of the thing),
2. phenomenon (what we perceive the thing through our senses, measurements, interpretations, which depend on our abilities to perceive, the accuracies of our instruments and senses), and
3. labels (the category that we place the phenomenon in our framework of world view). Love, lust, sin, etc, are labels of things greater than those words, or our understanding of them.
Labels are ladened with layers of traps for the unwary. It is why out of the mouths of babes come wisdom sometimes, because the innocence of youth cut through all the intellectual sophistry that trap the smartest who think they know the noumenon, when in fact they have been debating the labels - like how many angels dance on the head of a pin. It is this last use of labels that enslaves, and what I mean when I say that we need to be free of labels.
And to bring me back on topic:
"Ennis is gay" can be understood as
"(label of a person) (label of equivalence or label of membership) (label of category)"
The label of the person is easy enough. Ennis represents the person, and few of us would misunderstand the label for the actual person.
The label "is" requires more explanation to be useful because in English (and most natural languages) the word can be used for either one of these: 1. equivalence, 2. having properties of, or 3. being a member of a group. In this case, Ennis is gay implies the label is used for membership of a group AND has the property of "loving another man, a person of the same gender".
The label "gay" is both easy and difficult because it can have different layers of meaning. The easy meaning is "to love another person of the same gender", but the difficult meaning is associated with connotations that go with it. For example, "another person" in the case of Ennis is Jack AND ONLY JACK. This is different from other gay men. So is Ennis gay, or a special kind of gay? I have agreed in the past that Ennis is gay in that sense, but it means very little without a deeper understanding of the man.
"Ennis is gay" is about as meaningful as "Secretariat is a horse". It is true in some sense, but it takes away all the uniqueness and special qualities that make Secretariat a legend. The same is true to simply say "Ennis is gay", or "Brokeback Mountain is about two gay ranch hands." The statement takes away from the uniqueness of Ennis, and the special greatness of Brokeback Mountain. It is the taking away part that I object, not the part that is true.
I hope that clarifies my labels.
