This is likely the case with Sparta as well. Of course it had a very masculine culture, it had a legal system where women ended up getting most of the money. Eventually Sparta just declined into a very minor city and everybody else kind of just ignored it, there wasn't any explicit collapse I think but it was taken over by other powers.

Of course a system that allows women to hold positions of high power also means that other subversive actors would have been able to enter and exploit things as well. If the men of a society think that women doing a man's job is alright, they also would not object to an immoral outsider working in positions of power too. Since the end result would be similar either way.