When Raegan Zelaya and Shua Wilmot decided to include their pronouns at the end of their work emails, they thought they were doing a good thing: following what they viewed as an emerging professional standard, and also sending a message of inclusivity at the Christian university where they worked. But their bosses at Houghton University, in upstate New York, saw the matter very differently. Administrators at Houghton, which is affiliated with a conservative branch of the Methodist Church, asked Ms. Zelaya and Mr. Wilmot, two residence hall directors, to remove the words “she/her” and “he/him” from their email signatures, saying...