[GfBTWMmV]

"Most people would segregate themselves according to race"?

Of course not.

Most people would and do segregate themselves according to their tastes/ideology/personality etc. I really doubt a fascist white guy would be a friend of a leftist white guy only because they share the same race.

It is prohibited "to ask or give information about the race background of a person to rent or buy a house" because you are making money at the cost of providing a service to society.