Even Greener Pastures

I came across the word "Chinaman" in The Remains of the Day by Kazuo Ishiguro. A large part of the novel is set in the 1930s.
Miss Kenton and Mr Stevens are discussing "Chinamen" as objects (presumably statues?) and where they should be placed.

"Mr Stevens, I have just noticed something outside which puzzles me."
"What is that, Miss Kenton?"
"Was it his lordship's wish that the Chinaman on the upstairs landing should be exchanged with the one outside this door?"
"The Chinaman, Miss Kenton?"
...
"The Chinamen, I would suppose, were polished by someone then replaced incorrectly."

I felt there was a playfulness to the expression but didn't know how politically incorrect it would be considered these days.

What about the word "Englishman"? How do people from England feel about it these days?