About Masonic "Regularity"
First of all, you must be aware of something important about Freemasonry: there are two large families of Freemasons.
1- The first "family"
The first "family" of Freemasons is the largest all around the world. This is the group of Grand Lodges that are validated by the United Grand Lodge of England. They have specific requirements and landmarks that are shared by all of these Lodges and Grand Lodges. Among these rules, a few have been sources of numerous conflicts through the years. They are still applied even with some minor adaptations in some countries. They were fully published for the first time in 1856 by Dr. Albert Mackey. Among the most significant are the following:
Landmark 18th: the candidate shall be a man unmutilated, freeborn, and of mature age. That is to say, a woman, a cripple, or a slave, or one born in slavery, is disqualified for initiation into the rites of Freemasonry.
Landmark 19th: A belief in the existence of God as the Grand Architect of the Universe is one of the most important Landmarks of the Order. It has always been deemed essential that a denial of the existence of a Supreme and Superintending Power is an absolute disqualification for initiation.
Landmark 20th: Subsidiary to this belief in God, […] is the belief in a resurrection to a future life. […] To believe in Freemasonry, and not to believe in a resurrection, would be an absurd anomaly, which could only be excused by the reflection that he who thus confounded his belief and his skepticism, was so ignorant of the meaning of both theories as to have no rational foundation for his knowledge of either.
Even if the Grand Lodges are not currently keeping all the ancient landmarks, most of them still constitute the foundation of what is called their regularity. It is clear to anyone who reads these documents that they were written in a specific social and religious context. This is why some of them have been abandoned, and others reinterpreted. However, most of the three landmarks I highlighted before continue to be considered as absolute references, even with surprising choices. For example, it is common today to initiate someone who is disabled while continuing to decline any women candidates. It is also common to stick with the idea that Freemasonry is fundamentally rooted on Judeo-Christian values. In several large countries, this Masonic family continues to segregate according to beliefs. I must highlight a very important element to keep in mind. All these present rules, taboos, or segregations are the consequence of a politic of power coming from the government of these organizations. They are very rarely an opinion coming from the initiates. However, I should acknowledge that these kinds of principles are very rarely challenged.
This first family of Freemasons calls itself “Regular Masons” and considers the second family as “illegal” or “clandestine.” These words mean that it is unlawful to meet, talk or assemble with a Mason of the second family. If a regular Mason decides to assist a meeting of the second family or even to meet him privately, he will be declared a perjurer and expelled.
2- The second “family”
The second “family” of Freemasons is also present all around the world, even if the number of initiates is significantly less important than the first family. They are also organized in Grand Lodges. The requirements are sometimes different, sometimes the same as the first group. Women can be initiated in most of these organizations. This is the family which is declared “clandestine” by the first one.
My position about this question
In few words, I consider such segregation a shame and a demonstration of self-sufficiency. If someone has been initiated according masonic rituals coming from a genuine lineage, such initiate must be considered as a brother or a sister. All other considerations are a manifestation of intolerance, politics, or more. Choosing to initiate just men is different. This is a choice and should be respected, even if there is no logical justification. But considering that millions of Freemasons that are working in Grand Lodges coming from the 17th century as illegal should be considered as retrograde and a lack of education.
I am proud to have been first initiated in Europe in one of the oldest Egyptian Freemasonry. I am proud to have been a Grand Officer of the Grand Orient de France. I am proud to have received the degrees of the first family I was talking about. I met a lot of good masons in each family and a lot of masons intolerant and arrogant in both families.