This would be a much more compelling argument if I believed that homophobic politicians, judges, and groups will defend the speech rights of gay people. Instead what I see is a pattern of right wing groups leveraging the courts to protect their own right to hate while also leveraging the courts to oppress groups they hate. Standing up for the Nazi's right to march in my town won't cause those Nazis to stand up for my right to march in my town.
When’s the last time the courts protected the right to hate in the form of preventing speech of gay people? This is just worrying about things that don’t happen. Right now socially LGBT people have a moral high ground and very little of their speech is ever prevented.
How does it infringe on their right to speak though? They’re speaking very loudly about the issue in fact. I hear them more than I ever have in the past. For being less than 1% of the population I think they’re one of the most overrepresented speech groups, from what I’ve seen anyway.
And this is precisely why I do not expect any defense from the right. When discussion of gay people in classrooms and in books is verboten and when tame drag shows draw crowds brandishing weapons and laws banning them entirely, I don't see people on the right leaping to defense.
They are speaking loudly about the issue, because their speech is being infringed. The law in Florida currently says that you're not allowed to talk to school children about sexuality in an inappropriate way, without specifying what this exactly means. I have not seen any conservatives deny that this is specifically set up to still allow talk about heterosexuality (e.g. a male teacher talking about how he went hiking with his wife) while disallowing any mention of homosexuality (e.g. a male teacher talking about how he went hiking with his husband).
The only defense I can see would be the same which was used to deny gay marriage - "we're not infringing on their rights, they can still marry straight people of the opposite sex!" - which I'm sure we can all agree is not in any way a good defense.