"Travel is Dangerous," by Ed James, in CWA Anthology of Short Stories: Mystery Tour, edited by Martin Edwards, Orenda Books, 2017.
The one thing I don't understand about this story is why Edinburgh detectives would be shipped over to Glasgow in order to investigate a murder. There's no one closer than an hour away? Maybe it has something to do with the theme of the book being travel? All right, moving past that.
Cullen is a DS, detective sergeant in Scotland's capital. He is reluctantly paired with Bain, who complains that breakfast there is (as Cullen sarcastically summarizes) "nowhere near as good as in Glasgow, home of sectarian violence and divine fry-ups..."
A naked dead man has been found in a garbage bin. Well, not quite naked. He is wearing a pink diaper. The murder involved a gay orgy, which does not sit well with Bain. I can't find the exact phrase but at one point Cullen interrupts his speech "to prevent a hate crime being committed."
It's a witty story and various kinds of justice are administered before it ends.