I am still agog that someone does not see that the more formal "colored" is a different category of word than the more slangy "tranny."
"Colored" was a preferred, respectful term 75-100 years ago. That is the reason it was used in the musical. Because it was a non-offensive term, Hammerstein used to replace the n-word--which was the term Nellie used in Michner's book. If Nellie has used the n-word, Hammerstein felt the she would have lost much of the audience's sympathy.