Singular they has rapidly taken over to the point where it's now even used for persons where there is a presumed gender. While I may be fighting a losing battle, by god does it need fighting.
Why do you feel it needs fighting? I really don't think it's critically important to communicate gender with every use of a pronoun. We don't have separate pronouns for different races, young vs. old, short vs. tall, fat vs. skinny, smart vs. stupid, obstinate grammar nazi vs. speaker of contemporary english, etc., so what makes the detail of gender so important that it alone must be embedded in the pronoun? I really can't see a purpose for automatically referencing gender every time you refer to a person other than to reinforce sexism.
We don't have a "proper" gender-neutral singular pronoun, so we use "they" and "them" instead. It doesn't matter if this behavior has precedent dating back to the 1300s or if it started last week. What matters is that it's currently widespread and unambiguously understood by most (if not all) modern english speakers. The dictionary should be descriptive, not prescriptive. You are witnessing the evolution of language in action! Don't fight it, be fascinated and pleased!