Yeah, that’s the situation.
The specific reason she is going to lose is not because she said she didn’t want to live on the properly. It’s because neither RTTL nor the White community in Arkansas have any properly for sale. There is no violation of the Fair Housing Act if there is no property for sale.
The bigger question is whether or not Whites are allowed to freely associate like everyone else does, ie. can Whites have a Whites only, private member association. You’re right that denying Whites the right to do this would mean all the existing groups for Muslims, women, etc. would be illegal, so even if a judge tried to ban White only groups it would be overturned on appeal.
The problem for RTTL, and all of us, is that these legal battles still need to be fought and fighting them requires lots of money. That’s why they need a bit of help from the rest of us.