Welcome to the world of Bulverism in modern public discourse, where instead of actually answering your opponent's arguments, you assert that their position comes from some nefarious or irrational source, and their arguments can be ignored. This particular use seems to me to have raised Bulverism to something of an art form. By merely labeling anyone who is opposed to a homosexual lifestyle as 'homophobic', they have effectively dismissed those people's reasons for their position.
Of course, it's not like the left is the only ones who use Bulverism. That's the problem - every side uses it. As Lewis says, "Until Bulverism is crushed, reason can play no effective part in human affairs." When everyone uses Bulverism, focusing on the alleged motivations and psychology of their opponent's beliefs, no one actually uses reason to sort through the facts, logic, and assumptions of people's positions (or those few who do get drowned out by everyone else). Lewis again: "For Bulverism is a truly democratic game in the sense that all can play it all day long, and that it gives no unfair advantage to the small and offensive minority who reason."
It's not like the use of Bulverism by one side proves that their side is wrong (especially when all sides are using it). It's just that you don't really have a chance to rationally figure out who is right and who is wrong until Bulverism is no longer taken as a valid argument. And Bulverism isn't a valid argument - it's quite possible for someone's position to be correct despite potential bad motives for believing it (just as it's quite possible for someone to hold an incorrect position despite lofty and good motivations). You don't find out if someone's position is right by speculating on their motivation or psychology. You have to actually think and reason about the assumptions, facts, and logic of a proffered position (and endure their own analysis of your own assumptions, facts, and logic). Unfortunately, speculating about the motivations and psychology of your opponent is much easier, and, alas, often seen as more fun.
When Bulverism becomes as pervasive as it seems to have become, public discourse is no longer carried out on the basis of who can marshal the best facts, logic and argument for their side. It's carried out on the basis of who can portray their side as the most honorably motivated. In short, you no longer argue about who is right, but about who is righteous (and who is demonic). Sound familiar? Ultimately, it becomes a PR and marketing battle, and the prioritization of PR over real effectiveness has its typical corrupting effect.
This probably won't end unless we see a massive grassroots attack on the acceptance of Bulveristic argument. Contemplation of the likelihood of this actually happening are left as an exercise for the reader.