The NYT directed me to check out The Cylinder Preservation and Digitization Project, maintained by UC Santa Barbara. Way, way back in the day records were not flat platters but rather rotating cylinders. The good folks in Santa Barbara have digitized a bunch of these and you can listen to them streaming online or download them.
Lots of xylophones and banjos, lots of polkas and rags. And slurs, there's lots of those.
The site includes an admirable disclaimer about the popularity of "ethnic" songs at the turn of the last century and indicates that this terminology has not been sanitized from the original.
I tried searching for "pansy," "queer," "fairy," and "sissy." No luck. I'm not sure if this means that there aren't any such songs or that I don't have the correct terminology.
Terminology is a tough one. For instance, if you had to guess what the word was for minstrel songs, you might guess "race" or "negro" or even "colored." Fortunately the disclaimer points the way; unfortuantely the way is the word "coon."
97 results come up for "coon" including "That Welcome on the Mat Ain't for Me," "Everloving Spoonie Sam," and "Celebrating Day in Tennessee." I clicked on that last one, which the notes point out is described on the original sleeve as a "coon duet." One verse asks, "Why is every darky/feelin' kind of sparky?"
The site gives some weird insight into the state of both race relations and popular music back in the early 1900's. There are almost as many results for Irish--80-- as for coon. One song offers the helpful hint, "It Takes the Irish to Beat the Dutch."
No luck searching for "Jew," "Jewish," or "Hebrew," but I got 19 results with "Rabbi" including "Under the Matzos Tree," and "I'm a Yiddish Cowboy."
The site mentions that these cylinders cost $5 back in 1900, about $110 in today's dollars. So one must have had some especially strong feelings about those groups to shell out that kind of cash.
The links page suggests other sites, including the Canadian Virtual Gramophone, which is hardly free from slurs.