I've been reviewing threads on this board that I've missed. I don't know how I missed this one because the subject is one of my favorites. I haven't finished reading thru all the posts but there are lots of great ideas.
My own idea of what Jacks black and Ennis's white hat I posted long long ago on IMDB. In the Western film genre the good guy, the hero frequently wore a white hat and the bad guy a black hat. So much so that it became a cinematic trope, the audience would know who the hero was and who the villain was instantly, especially in a silent film. In later westerns of the 50's and 60's the good guy is usually just trying to make an honest life for himself as a rancher, or farmer, or just trying to keep the peace in his little community as the sheriff. The black hat is the one who starts the plot moving. He's the one who instigates the action. The white hat is threatened in some way and must respond in an effort to return things to the way they where before the black hat showed up. And usually the white hat would get the girl too in the end, so he'd have it all. The white hat would also come to a greater understanding of himself and those around him; the woman he loves the other inhabitants of his community and even of the black hat.
In BBM Jack being the black hat instigates the action which drives the film forward. He is the 1st to put out his hand to Ennis and introduce himself, he leads the way to the bar, he draws Ennis out of his shell, he instigates the sex, he instigates the reunion, he suggests the cow and calf operation. Ennis in contrast as the white hat is simply trying to live his life as best he can and to him that means conforming to what western society claims as a proper life: Married with kids, a hard worker competent at what he does. Heterosexual. He needs to be the stoic cowboy. Jack throws a wrench into all of that and Ennis must reject him, at least at the end of the summer of '63. Later Jack reappears and Ennis engages with him, again he rejects him, but only partially and tries to have it both ways. In the end Ennis wind's up where he started; alone and still poor. But he does have his daughter's. He's also learned something about himself and Jack along the way.