For this situation they and their can be used. It have been accepted usage for a long time.

These pronouns have always been a nuisance, as I can personally testify. But it is the worst when we resort to the clunky “he or she” or “him or her” to refer to a person whose gender is unclear. “When the speaker introduces him or herself,” for example. I’m ready to liberate myself from the co…
Goodbye, Preferred Pronouns
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Victoria Z.
B. O. Face
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Oct 14, 2022
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For this situation they and their can be used. It have been accepted usage for a long time.
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Written by B. O. Face2.9K Followers
·1K Following
No woman ever murdered her husband while he was washing the dishes.
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