Its usage in the song is not derogatory. It's meant to highlight the offensiveness of it and to cast the speaker as one of the disenfranchised of America.

It's controversial, I suppose, but it's meant to make a point. Changing it would just diminish it.

As the other commenter said, it's not derogatory. He's taking a word that's been used to belittle and dismiss him and people that share his views, owning it, and using it to fire back against those that would use it against him in that way.

Basically, "Call me gay* (ok, like that's supposed to be a bad thing? Watch me call myself gay lol) but at least I'm not a dumb idiot follower of the redneck/MAGA agenda."

To me, it's like a more sophisticated "I know you are but what am I?", if you will. He's so unphased by the label that he uses it for himself with little hesitation, thus stripping its power as an insult against him. Hence why he fires back with a new, more critical put-down. It's meant to hit them (someone that would call someone else gay or a faggot* as an insult) where it hurts, in the same way that person has meant to hurt others by using those terms derogatorily. He's literally naming and shaming the bigotry of the time.

*And yes I know the term faggot has some nasty origins, but it was colloquially just a much more rude/derogatory way to say "gay person" when this song came out. I highly doubt the majority of people that used it were actually thinking that critically about it. The song itself at least very clearly does not mean it in the original sense.

You should hear him sing King for a Day.