Inhabitatio Dei finds some precedents with clout for using “they” rather than “he” or “she” as a pronoun for a general human being without gender specified:
Here are just a few samples of “they” being used as a universal singular pronoun in Western literature:
— Shakespeare: and every one to rest themselves betake;
— Jane Austen: I would have everybody marry if they can do it properly;
— W. H. Auden: it is too hideous for anyone in their senses to buy;
— Shakespeare: ’tis meet that some more audience than a mother, since nature makes them partial, should o’erhear the speech;
— W. M. Thackeray: a person can’t help their birth;
— G. B. Shaw: no man goes to battle to be killed. — But they do get killed;
– From Merriam Webster
All this to say, using “they” as a universal singular pronoun is not bad English whatsoever, nor is it grammatically problematic. Strangely then, it seems to me that the only reason for rejecting a grammatically-appropriate gender-accurate pronoun in favor of a male one would be . . . ideological. Imagine that.
As a huge fan of they’s ability to get the job done without sexist connotations, I am delighted to see these examples of the usage’s long history.