The Childress Dancehall Banner says 1978 and the scene where Ennis meets Cassie is directly the one before. The STS also names 1978 as the year Ennis meets Cassie, so they have dated for five years before the tell you what conversation. Same goes for Jack and Randall.
But five years are hard to believe, aren't they? This would make the conversation by the lakeside very odd and additionally, it would make Ennis's way to break up with Cassie somehow implausible. After
five years of relationship (even if it wasn't the closest), one would rather think something has happened to your lover than contemplate the possibility he has dumped you if you don't hear anything from him. I think Cassie would have been worried about Ennis and not come to the conclusion he dumped her.
And since Cassie was a somewhat "pushy" type, I'm sure she would have sat on the steps of Ennis's trailer one night and would not have settled with some unanswered notes. I think she just would not have "gotten" the message and second, would have demanded an explanation even if she had an inkling about possibly being dumped.
But if they had been together much shorter, then it would make sense. Ennis's way to dump Cassie and his indifferent way of speaking of her make much more sense if they had known each other only for a relative short period of time.
The timeline is really such a tricky subject
.
On the OP: we have not one iota of information about her being homophobic (or not homophobic). Like indeedcrayons already said: it's a non-issue in the movie.