There are a significant amount of people who care about gender such that it makes sense for landlords to discriminate by shared unit. They should have a mix of male only and female only units. (and if they want mix units). In the US not enough people care about the religion of their roommate to be worthwhile trying to find a fair solution to those who care (if you do care you can ask at your church).

It is important to ensure that when you allow such discrimination it is by unit and that landlords not be allowed to discriminate overall

The problem currently isn't the landlords, but the tenants and subtenants. Maybe if landlords could offer more shared housing, this problem would go away. But tenants frequently look for people of the same gender or race to rent a shared housing.

The other (smaller) issue I think is house hackers (landlord occupied properties). The landlord doesn't own multiple units and is effectively "airbnb-ing" out rooms for short term leases.