The reason those organizations are not recognized is because they are at cross purposes. OES is to masonry as the girl scouts were to boy scouts.
Just what are men gatekeeping when they associate with each other without women, other than maybe their own attention? If you want better men, they need to learn it from each other.
but OES is not masonry, or is it? if it is, then it should also be allowed to use that name.
i am not against male only groups, i just don't like male (or female) only groups claiming a domain for themselves. if there are male only masonry groups, there should also be female or mixed masonry groups. just like we have male and female and mixed soccer groups or other sports. nobody should be saying that women are not allowed to do something as such an activity is reserved for men. (and the reverse)
boy scouts and girl scouts are explicitly recognizing each other as two different forms of the same activity. saying that girl scouts are not recognized as boy scouts makes no sense. both are scouts (even in countries where the girls call themselves guides)
but you said above that mixed lodges are not recognized. that makes no sense to me, unless they deviate from the ideal of masonry in other ways than just gender. unrecognized scout groups do exist too, for various reasons. the gender of their members is not one of them.
It's not gender, it's sex, and the organizations are different because sexes are different. The things that make men better men don't necessarily make women better women, and vice versa. This idea of men and women being social constructs, as opposed to some sexless personhood eunuch with gendered attributes being a social construct, is not consistent with an objective reality. The idea behind these organizations is they are for men and women in support of a social fabric that provides peace and stability, and not say, permanent revolution and chaos.
Just what are men gatekeeping when they associate with each other without women, other than maybe their own attention? If you want better men, they need to learn it from each other.