Investigation of non-binary American prospective member
The term “co-Masonry” refers to a cooperation between sexes. The question ‘what about somebody who does not regard himself either man or woman’ is a fairly recent one in public discussions, but I think it is safe to say that co-Masonic lodges have always been open to any gender. Of course also this website spoke of ‘Freemasonry for men and women’ to indicate inclusiveness and this description was (is) still used on many places, but I doubt it has ever been thought up to indicate exclusiveness in the same way that ‘traditional’ Freemasonry speaks of members that have to be male.
Be that as it may, a prospective non-binary American seeks to join a lodge and asked around a bit with mainly two questions. The first is: can I join? The second: how would I be addressed?
The Universal Order of co-Masonry has the line “Freemasonry for Men and Women” on their website, but they confirmed (unsurprisingly) that non-binary people can join. As this organisation refers to every member as “Brother”, they don’t really have to think about question two.
Also the American federation of Le Droit Humain uses the line and also confirmed (unsurprisingly) that membership is possible. Two of their lodges actually address both questions on their websites:

I wonder how many lodges have thought this through so far, but I’m sure that the closing line will be what any lodge advocates.
The membership question isn’t really hard to answer. I doubt that there will be any lodge that will not say: “Of course you’re welcome to join.”
The addressing issue will probably be something between the (prospective) member and the lodge until the time that the need rises to harmonise the use over lodges.
To whom it may concern
Freemasonry is traditionally male-only. Since 1893 there have been lodges that are not gender-exclusive. To indicate the difference, the description “Freemasonry for men and women” has for a long time been used and it still fairly common, but this description is meant to be inclusive, not exclusive, even if the wording is no longer entirely fit in our day and age.
If you are interested to join, get in contact with a mixed gender lodge and proceed from there. I doubt non-binarity will every be an issue.