Constructively, when it comes to culture building in a setting (RPG or not), one thing to keep in mind is that the culture that you're building should definitely fit within the setting you're building it for. All too often I see people try to shoehorn make-believe cultures based on the author's wants, based on their cultural perceptions of our world, and it just always comes across as heavy handed as fuck.
Secondly, especially in an RP setting that you intend to be open to others, I always suggest a certain disconnect of self from the culture. If it turns too much into "playing house", the author is going to find out that others aren't "doing it right" or other players attempting to leave their mark on the culture might be met with negativity.
Fifth World had some great cultures. When people made a culture, many of them seemed to be based on the cultural result of the surrounding geography, so you ended up with a seafaring culture in a sci-fi age, and some cool ones built around how living in the shadows of ash and volcanic surroundings would affect the mentality of the people. What's important to them? RAIN? Cleanliness? Neat stuff like the way Fremen reacted to water.
Concepts regarding gender equality are subjective and prone to political argument, but as a whole I don't see many players having issues with matriarchy. So, after reading your initial idea, my critique is this: If you're going to write a feminist idea into a setting, you need to constantly ask yourself "why?"
- Why would a goddess favor women over men?
- Why are women better at things than men?
- What is an honest, male-viewpoint in this culture's reaction to this? Wouldn't some feel neglected? Ambitious? That they have a glass ceiling? Do they worship other gods? If the culture is female-centric right down to religion, trade, etc, then what do male children study?
(Realistically, or logically, there would be impact)
If you find yourself having to ignore answering these questions, then you're not really creating a culture, but could be instead creating a sandbox roleplay idea tailored to your own personal preferences.