Now I'm not saying I don't see a need for it. I understand the purpose. I just don't like the mess it's made of things grammatically. Instead of saying, "If someone left his lunch here, he should pick it up tonight", we're stuck with saying "If someone left his or her lunch here, he or she should pick it up tonight." If writing, or have a few seconds to reformulate the sentence before speaking, we can say, "If someone left a lunch here, it should be picked up tonight." Usually what we end up with is, "If someone left their lunch here, they should pick it up tonight." UGH!
I'm reading a book by a university professor, "one of the world's leading Bible scholars", and was distracted by this phrase: "Such a person is deceiving themselves." Really? If he'd written "himself", would the gender neutrality police have swooped in on him? Would anyone truly have presumed he meant only men?
Some sources tell me that mixing singular and plural pronouns is now considered acceptable. Guess what? I even find myself doing it myself, much to my chagrin. I'll find myself in the middle of a sentence with three choices: back up and start over, follow through with an awkward he/she, his/her construction, or grit my teeth and listen to myself say, "I won't give the person's name in order to protect their privacy." It might be acceptable, but it's like fingernails on a blackboard.