[smsm42]

> a story has been going around that a court has put a stay on the executive order.

That story is false (at least as far as I know). The stay was put on one detail of the implementation of the order, not the whole order - namely, on deporting green card holders that has already arrived in US airports.

See: https://en.wikipedia.org/wiki/Darweesh_v._Trump

> Having said that, my understanding is that the referenced court case only applies to the specific individuals who sued

ACLU is seeking class action status, but in the meantime if several judges agreed that the stay is warranted I imagine it would be not hard for any person (with access to law assistance etc. of course) to be able to obtain similar order.