I don’t see a reason why they shouldn’t, as AFAIK women can participate in rituals.

https://en.m.wikipedia.org/wiki/Freemasonry_and_women

Section: Recognition of Women as Freemasons

In short, in some places women are accepted and in some they are not. As the Unified Grand Lodge of England does not recognise women as freemasons, women are not officially capable of reaching the 33rd degree. However, where women are recognized (i.e in Continental Freemasonry), women should be able to reach the 33rd degree.

Some quick research send like it highly depends on the lodge. From Wikipedia

Grand Orient de France, in addition to recognising women’s masonry, decided in 2010 that there was no reason that its lodges should not be able to initiate women, thus adding another strand to international co-masonry

So it seems some do allow for co-ed rituals such as initiation. That said the whole thing sounds pretty sexist to me. I’d probably just avoid the whole organization or any ties to them. No reason to give that group more power.