Google has been running a campaign for two years about gay rights and discouraging 'homophobia' (https://www.google.com/diversity/legalise-love.html). Also, three main sponsors of Olympics including AT&T have also spoken out against Russian laws.
It's a good word for it. It has an established meaning, it is universally understood, etc etc. The fundamental use of language is to communicate, and I don't really think homophobia fails in this respect. There are plenty of non-"good" words for other things in the English language that get used very often without people quoting them or complaining about their use.
As an example though, I'm not a pedophileaphobe - I'm not afraid of pedophiles. I think what they do is wrong.
The number of people who are "afraid" of homosexuals is miniscule. Most people who you'd label "homophobic" actually just believe that homosexuality is wrong, not that it's scary.
They are not scared of homosexuals, but of homosexuality. It represents a threat to set values and a set way of living to certain individuals. If it wasn't considered a threat to those values, why suppress it? It's homophobia.
