Writing Queer Relationships, Part I

In Fictionland, a surprising number of characters seem to undergo a personality transplant when they fall into True Love. However, this seems to present a particular problem for any characters who enter a relationship with someone of their own gender. These relationships also have a tendency to fall into a warped parallel universe where all their problems stem exclusively from the gender of the characters involved, rather than the sorts of relationship problems which occur in real life.

Now, this is not to say that your same-sex couple won't potentially face some extra challenges. Perhaps people in your story's setting aren't too keen on such relationships. If that's the case, the reason needs to make sense in-universe. Maybe your fantasy country got devastated by a magical plague and any non-procreative sex is frowned upon due to the dire need to repopulate. Maybe there's a religious issue (though this should be fairly thought-through and make sense in cultural context). Even then, your characters should have normal relationship issues, as well as outside pressure. 
That said, remember that homophobia does not have to be the default. If you're writing a fantasy world from scratch, you make the rules. It might make complete sense for the citizens of your fictional society not to care about the genders of the people in a relationship (or even to care about gender, or two-person monogamous relationships... maybe they're all non-gendered and form polyamorous multi-sex family groups. It's your magical/alien/fantastic species, after all).

Furthermore, if you're writing historical fiction, do your research. Attitudes towards same-gender relationships have varied widely, and even within the same time and place, factors such as religion, race and social class may play into people's attitudes. For example, in 18th century England,  gay men were persecuted among the upper classes, but tolerated by the poor and working class (lesbians were ignored by everyone). In ancient China, having a same-sex 'piece on the side' was okay, as long as you procreated and passed on the family name. A good research session can turn up some subtleties which will make for a much more nuanced setting than recycling the clifnotes version of modern Western homophobia.