I've just read your story and I loved it. No, it's not racist at all, on the contrary... it depicts very well a certain homophobia in the character who says:
“I’m sure they keep some back for people like you.”
You are allowed to depict homophobic behaviour in characters to show their character and flaws. What you should never do is depict homophobic behaviour as correct or acceptable. And you make that clear in the next lines, by showing the true feelings of the first person narrator in the next sentence and next paragraphs:
"Ah yes, people like you. That cut me, even though it was aimed at the mother."
It's clear the homophobia is not supported anywhere in the story. The sympathy of the narrator (and the readers') goes to the victim.
I've just read an article about readers who confuse flawed fictional characters with the writer who created them. Says something about the reading level of some people...
As to the other question: is the story cultural appropriation?
I don't think it is, because you live in a country where (unfortunately) this kind of story happens every day, and every hour of every day... and you've heard of it yourself. The only "appropriation" is in choosing to tell this story through a first person narrative, when you (as writer) are a different person from the muslim narrator. But I don't think there are any rules about not writing fiction in first person narrative unless the writer is the same person as the narrator. Or are there?...