The best we've come up with is singularizing "they"/"them"/"their",
Which is hardly a new development. The OED has numerous supporting quotations showing common use of singular "they" back to the 1500s and singular "their" to the 1300s. This goes back so far that the earliest examples are barely recognizable as English. The OED does note on one of the entries that the usage is "not favoured by grammarians".
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