Often, Jewish organizations have as a contract clause that employees agree to take issues to beit din and not (or at least, before) secular courts. But if the employee is not Jewish, is that employee's first recourse still required to be beit din? I'm not sure if this is a question of law (the validity of the religious court as a viable option recognized by the US legal system and the contract's clause still being binding) or one of halacha (does the beit din have authority over a non-Jewish party).
Journal of the Beth Din of America 1:1, page 32:
My understanding is that sometimes a non-Jewish party will agree to use a beit din -- compared to the regular courts, it can be faster, cheaper, more confidential, and/or it's more likely that the Jewish party will be compliant.
As I understand it, though I am not a lawyer, an employment clause can say "issues shall be settled by Arbitration Panel XYZ", and if people sign that, they would have to go (at least initially) to Arbitration Panel XYZ. Generally a beit din is recognized by the government as an arbitration panel if both parties agree to use it.