So I've been playing with the Gender civic in my mod and here is what I have right now. First a few things to bear in mind. I am using religeous options in some of the early gender civic, I like the idea of two catagories affecting religeon and gender is not a bad secondary choice. Optimizer, you mentioned wanting to emphasize religeous struggles and this approximates this somewhat as religeons loose some power as you switch over to modern gender civics. I also like these bonuses because I don't think it's entirely unreasonable to say religeon enforces gender roles. So here is what I have right now...
Patriarchy - Default Civic - Lowest Cost (I changed all the default Civics to half of Low cost so they are more attractive. It also offsets the costs of having a 6th catagory)
No effects
No real changes here, I think it makes sense for the default
Matriarchy - Pottery - Low Cost
+2 Health
+10% Building Production in City's with State Religeon
Less happy here, there isn't much to go on for matriarchy but I definettely think it should be included. I could easily swap the health bonus for something else but I kinda like the Religeon effect. Pottery also isn't a great discovery tech but Agriculture is a start tech which I don't like and nothing else quite works.
Polygyny - Monarchy - High Cost
+100% Cottage, etc. Growth
+25% Unit Production with State Religeon
Monarchy is little late but I think it's appropriate, this is a powerful Civic. So the Growth bonus just seemed nessicary and appropriate and the Unit production is nice because it not only helps with military but I am pretty sure should also affect Settlers and Workers, thus helping your overall Growth. Overall these make Polygyny worth its High Cost and I wanted atleast one High Cost civic for Gender. Aside from the lateness of Monarchy I love how this one came out.
Equal Rights - Democracy - Medium Cost
+50% Great People rate

Penalty for Civs without Equal Rights
+3 Happiness with Hospital
Another favorite of mine. Like I said before I don't think we need this and Sexual Freedom so I stole the Hospital bonus from Birth Control and applied it here. Equal Rights are good in and of themself but once contraception and anti-STD pharmaceuticals are avalible you get the full benefits of that sexual freedom. Making one civic for this also let me use the happiness penalty, I felt it's appropriate here, this is the only gender civic I have that grants all citizens total control of their sexual identity. I have too much fun causing unrest in my unenlightened neighbors.
Birth Control - Medicine - Medium Cost
Unlimited Engineer and Scientist
Produce Military Units with Population
Here Birth Control means state Birth Control, the society dictates who reproduces, when and how to control its population levels. Its a hard effect to represent in game so here it basicaly takes the form of giving you population control options as a player. Militart Units are produced faster at the cost of city growth (great idea Optimizer) and Engineers and Scientists don't produce food while still helping your cities. It may piss of citizens used to more freedom but you can find ways to manage that unrest.
Finally I am going to have 6 civics in 6 catagories in the mod I am making so I do want another gender civic, I probably will bring back something like Recongnition since I don't have a "somewhat equal" early civic avalible and that really seems to call out as what is missing from my set up.