According to Fiqh of Shia Islam it is permitted.
According to Islam any human potentially has duty to research about existence of God and then about religion and and if do a real and serious research will finally become a Muslim. because in fact God exists and currently the only accepted religion in view of God is Islam. although Judaism was accepted before prophet Jesus (PBUH) and Christianity was accepted before Prophet Muhammad (SAWW) but they are not accepted today because they are deviated today and Islam is sent by God as a perfect and updated religion.
In Islamic view if a couple marry according to their own religion they are considered married and couple in Islam view although they are not Muslim. this means that for example if a non Muslim married couple convert to Islam their marriage is considered legal and there is no new marriage needed based on Islamic rules.
A non-Muslim male and a non-Muslim female can marry based on their own religion and laws and this marriage is considered legal in Islam if their own religion consider it legal.
Online answering of Official website of Grand Ayatollah Makarem Shirazi