Homosexuality isn't intrinsically an atheist issue. Some support gay people, some don't. Other metrics exist as to whether a particular atheist does support homosexual issues, or not.

Atheists tend to support the LGBQ community, more often than not, because, once theism is removed from the equation (and thus forming a secular framework), there's no good reason to oppose gay marriage, for example, within the context of atheism versus theism. Atheists are likely to adopt Secular Humanism.

Also, atheists tend to find themselves side-by-side with other minorities in defending their rights, so we tend to be allies against many religious groups. LGBQ individuals, as a minority, are victimized frequently, alongside atheists.

Note: As of July 2019, you may notice that the "T" was dropped from "LGBTQ"+. The atheist community seems to still struggle significantly with not being bigots against the transgender community, so we can't say with integrity that it's supported. Maybe one day the "T" will be earned again.