Here's the issue: Freemasonry was seen as very successful and popular among all levels of society in the 18th and 19th centuries, but, while many men wanted membership in the Fraternity for a multitude of reasons, not all men were admitted. In other cases, men joined and later decided they no longer wanted to be members or were suspended/expelled.
This led to two major developments:
(1) the development of non-related non-Masonic organizations that were modeled on the "Lodge system". Some of these organizations became quite famous: the Grange, the Elks, the Eagles, the Knights of Columbus, and the entire Greek college fraternity-sorority system among them. Most you've never heard of because they were limited to specific regions or were so short-lived they never had the time to make a mark on history. These organizations provided social outlets, opportunities for civic involvement, political connections, life insurance, etc. These organizations claim no connection to the Craft and have typically many members in common with the Masonic Lodge (talk to your fellow Masons; many of them are also in the Rotary, the Elks, the Optimists, etc., all of which fall into this category).
(2) the development of what we typically call "pseudo-Masonic organizations" that take a typically-Lodge-like system and focus on the darkest parts of esotericism and base their rituals on bastardizations of Masonic and Masonic-like rituals. These organizations include (but, as above, are not limited to): Thelema, the Ordo Templi Orientis, the Golden Dawn, and the Rite of Memphis-Misraim (In fact, the 95 or 99 degrees of the Rite of M-M take the names of their first 33 degrees mostly from the Ancient and Accepted Rite of Freemasonry, although there was not a direct connection between the two organizations). Many of these organizations claimed connection to the Masonic Order and some were actually started by Lodges that became clandestine by Masonic practice. And you may find a few members of the Masonic Lodge that are a part of these organizations, but they usually have a hard time getting into recognized Lodges due to their...unusual...religious beliefs. It's also worth noting that Crowley was a member of such a Masonic Lodge (as mentioned above), as was Generalissimo Antonio Lopez de Santa Anna, former President of the Republic of Mexico and "Butcher of the Alamo", among many other derisive titles he tends to possess in those lands that use to fall under Mexican rule. I mention this because you often hear both of these men referred to as Masons, when the reality is that they were both clandestine Masons, thus not part of recognized Masonry (I know, good luck explaining the rules of Masonic recognition to those who are not members of the Craft and are often simply out to besmirch its character).
As for co-Masonry, my understanding is that co-Masonry is not recognized by any regular Grand Lodge (the reason for this is due to the fact that they recognize both men and women as "Master Masons", which is strictly forbidden by UGLE and, thus, by all of the Grand Lodges in fraternal concordance with UGLE, which obviously includes both the Grand Lodge of Texas and Prince Hall Grand Lodge of Texas). However, Adoptive Masonic orders (such as the Eastern Star, Amaranth, White Shrine of Jerusalem, etc.) are recognized in many Grand Lodges (although not part of Freemasonry, they do require regular Masonic connection for female members and regular Masonic membership for male members).
TU