Saying that the singular use of "they" is ungrammatical ought, I think, to be construed as incorrect.
Grammar is not a set of rules by which one should speak or write but a description of how this is done. If the grammar says "they" is wrong, then clearly the grammar is wrong and needs rewriting.
After all, "the use of the plural "you" for the singular "thou" was once thought to be ungrammaticla.
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sj