If a gov. authority can make it illegal for any private business to conduct checks on past history and/or criminal histories of prospective clients, then virtually any business could be liable to those strictures.
Own a lending institution where the integrity of the people handling other people's money is vital? Well then, you have to hire embezzlers, bank robbers, burglars, etc.
I would think not being allowed to check on the past history of clients whether they're renters or whatever would be unconstitutional. But now with our "living, breathing" constitution as defined by liberals anything is possible.