I love Georgette Heyer, but the reasons you mentioned are exactly why I don't read her detective stories. I can deal with the classism and sexism and racism (sort of; I also avoid The Grand Sophy) by thinking of her books as fantasies, which they might as well be for me.

Speaking of crossdressing characters, I just finished reading Amanda Quick's Burning Lamp (genre romance with fantasy bits) which is set in Victorian London and has as minor characters two men who are actually women (and presumably in a relationship, but it's never said). I think one's a crime lord.