Hello, and thank you for caring enough to ask!
For me (and please? I'm speaking only for myself

not the greater population of lesbians)...
Homophobia is a little more involved than being anti-gay marriage. Sometimes, someone speaks out against same gendered marriage, but is really covering for their complete intolerance for anything lesbian or gay.
Why wouldn't someone want to allow two adults to marry? No one is advocating that those adults get married in a religion that doesn't want them. Go ahead and try to marry in a Roman Catholic church if you are not RC, or willing to convert, or be willing to raise your children as RC? That's an excuse and those who use that excuse (that all religions will be forced to perform marriages) to me are deliberately fear mongering. There is no truth to it.
Homophobia consists of those people who are intolerant and don't care who knows it, like the man who passed me (and my Rainbow Mickey and HRC stickers) on 75 and flipped me off while driving beside me for several miles... that's homophobia too.
Homophobia is demonstrated by those people who refuse to accept that two men can have as loving and honorable marriage/relationship as a man and a woman. Homophobia is cutesy sometimes too. Two men are disgusting, but can we watch you two women? Yes, that is real. Yes, those sorts of questions do get asked.
Homophobia is any level of feeling that someone is less than another solely because of who and what they are (within this context). We call it other things when it's race or gender based, don't we?
Intolerance for accepting that my life is as valid and imporant as your's.

That my long term relationship with the woman I call my wife is as valid and important, and beautiful as is any opposite gendered relationship.
I'm sure there are others here who will be more profound, more succinct, more thorough, but these are some of my thoughts on the topic.
Again, thank you! I truly appreciate your asking.
Take care now and don't hesitate for one second to ask for clarification of anything I've written.