AJ: I have no idea about the background of the Williamsburg lawsuit you and Syag refer to but the only time it is permissible to engage in arkois is when a Beis Din first issues a Heter Arkois. That’s generally only possible if the other party failed to respond to a B”D hazmana. Presumably this is what occurred in that case.
Nevertheless, the idea that a Jew may civilly sue another Jew in non-Jewish courts without first seeking to resolve the case in Beis Din has no basis in Halacha and is unquestionably prohibited m’doraisa. So the idea that it is okay to initiate a lawsuit in secular court clearly indicates that person is irreligious/non-Orthodox even if they claim otherwise, no less so than if they eat pork.