Allow me to criticize a bit.

> women on nostr want to form a group to chat without men? Yes please! Users dedicated to using your client that speak in ways cohesive to you? By all means! Specialized group wanting an interoperable community with other communities? Of course.
> 
> Have white list relays to connect to pull in from select relays for your feed and not broadcast your notes to all relays at once.

If that's the goal, Why not spin up an mastodon / pleroma / web forum instance instead?

Nostr goal is different from what you've mentioned above. It tries to receive information as much as possible & most of the time is not for forming a single group or similar. 

 If you avoid the platform that i suggested & prefer to be on nostr,

Spin up an relay,
Suggest every single womans to ONLY CONNECT TO THAT SINGLE relay.

Hooray.
Centralized network. There you go. 

 But still i won't get why you don't spin up these platforms that i suggest instead. These are suited well for your purpose. 

 The additional benifit is that your identity and followers don't need to be tethered to a single server like centralized social media or the fediverse. It is a gradient of optionality. 

 Optionality not afforded by any other system. 

 The point is that nostr can encompass any level of openness you care for. it doesn't need to be wide open all the time. From that, centralized social media's or the fediverse's functionality is a subset of what nostr can do - with even simpler implementation.

We already have private and paid relays, but they are just thrown into the soup without any differentiation. 

 The problem is that everything is wide open (for real, on protocol's end) in nostr. You couldn't really adjust that.

Still, Don't fediverse could do the same exact thing? Being half open or similar? Because other users from external server still could give a follow.