I know I am out of touch socially sometimes, but I have never seen anyone of any political leaning assert that the word "homophobic" is inaccurate, inciting, or misused when referring to a person or a law that treats someone negatively because they are homosexual.
Many of these “public accommodation” type arguments are coming up in the context of highly religious people who provide services not wanting to create works that celebrate gay marriage. These people are often described as “homophobic” even though they would say that they are not; they don’t have an “irrational fear or aversion to homosexuality or homosexuals”, they simply don’t think that the living arrangements they want to pursue are either moral or practical, and thus would prefer not to participate in them.
If you believe this sort of thing about yourself, e.g. that your objection to whatever a particular policy is a carefully considered opinion that you’ve thought about and is informed by moral principles and/or facts, then being described as “homophobic” is going to appear to be an extremely lazy way to skip past discussing the merit of that opinion and the principles and facts that were used to form it and instead attack you for holding that opinion in the first place. It may even be an actual argument ad hominem, depending on how the exchange unfolds.
Your mileage may vary on whether or not you would or should agree with this hypothetical person I’ve constructed who would object to being called homophobic. I personally avoid using the term to describe other people’s ideas or laws whenever I find myself debating someone who is opposed to gay marriage, because I find that doing so makes it harder to persuade someone that they should change their view. Calling someone a bigot is somewhat insulting, and nobody was ever insulted into changing their opinion, but lots of people have changed their view on gay marriage over the past two decades.