People who say "They isn't meant to be singular" are just as annoying as people who say they hate the word "Moist".
No. You don't hate the word moist. If it really makes you uncomfortable then that's because you're choosing to see it in a weird way. Like getting weirded out by a child innocently calling their parents "mommy" or "daddy". You're the weird one, there's nothing wrong with the word moist.
And "they" has been used as a singular pronoun since the 14th century. If you've been taught it isn't, then the person who taught you is ignorant. By definition it is used as a plural and singular pronoun.
They're equally annoying because their reasoning for these things is just ridiculous. One rooted in a dumb trend and the other in genuine incorrectness.