...even stating that Shakespeare wouldn't have used "they" if he knew the gender of the person he referred to.

I literally gave two examples of him doing so. What are you talking about?

Sure, they aren't referring to any specific person, but the gender is clearly stated. Your prior reasoning was that it was improper if the gender is known, not if the person is known. Stop shifting goalposts and just accept new information when it's presented.

As an added note I don't think it makes a difference if the current use is new or not, and it shouldn't matter in this debate. Language changes all the time, even if people resist it.

Yes, that's correct. Someone was the first to use singular they. The argument about being grammatically correct is fairly stupid, because it's clear it is now. However, some people make an appeal to tradition saying it wasn't but it always has been for as long as they've been alive.