Using “their” instead of he or she, does anyone else struggle to accept this?

Today I read an article about Demi Lovato shaving her head and the whole way through I struggled with the fact “they” or “their” was used instead of she. This article was grammatically incorrect due to this and therefore I’m wondering if it’s really OK to refer to someone as they instead of he/she if it stuffs up the way we teach the English language and how things are written. I don’t mind if someone wants to change from a he to a she or vice versa but isn’t “they” or “their” going too far? Here is a copy of the article, see what you think.

www.instyle.com/.../demi-lovato-buzz-cut
Using “their” instead of he or she, does anyone else struggle to accept this?
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