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It's been used since the time of Jane Austen (by Jane Austen, in fact), it's perfectly normal: https://pemberley.com/janeinfo/austheir.html

Curiously, the page you've linked explains that it isn't normal to use it in this case: "can only be used with a morphologically and syntactically singular antecedent when what it refers to is semantically collective and/or generic and/or indefinite and/or unknown".

I don't even notice it anymore.

Then please help normalize it, instead of worrying about hurting the illiterate feelings of those who find it unacceptable.