This topic has been reposted in various forms, repeatedly. And if you want to comment on the Church restricting women, they were not alone. Here is a taste, it even describes the historian F. Cumont who is cited above:
THE EXCLUSION OF WOMEN IN THE MITHRAIC
MYSTERIES: ANCIENT OR MODERN?
JONATHAN DAVID
The following paper deals with the scholarly supposition that females were
excluded from the ancient mystery cult of Mithraism. This notion has been part
of scholarly dialogue about the religion since Franz Cumont, the father of modern
Mithraic studies, introduced it in the late nineteenth century. Though many of his
conclusions about Mithraism have been challenged or refuted in the past thirty
years, the particular idea that the cult excluded women has persisted?
In fact, most of the early Christian Church?s members were women because of their relatively positive POV concerning the female gender.
Anyway, my first point is that a hell of a lot has changed in the historiography since the late-nineteenth and early twentieth-century concerning cultural anthropology and religious studies. The emergence of Neo-Paganism to name one issue out of many. Why posters keep citing articles from hack writers that use such out-dated and disproved theories is beyond me. I'm surprised that nobody has sourced George Frazer yet, at least as far as I know.
Secondly, what does it matter if the dating surrounding Christmas is pagan? Even religious intellectuals from roughly the same time as Cumont, like Lewis and Tolkien, had no problem reconciling pagan mythology with Christianity. They simply saw Christianity as fulfilling paganism. Next thing I'm sure some Captain Obvious will post the ground-breaking news that Christianity derives predominantly from Judaism!