This is a strawman. The homeless schizophrenic is clearly not capable of caring for themselves, so their inability to participate in society should not impose restrictions on all businesses.
The problem you cite is not solved by requiring businesses to accept cash—it is solved by removing the homeless schizophrenic from the depravity of the street.
Many people at the margin don't have bank accounts. Not only schizophrenics, but undocumented immigrants or the homeless. There are a lot of undocumented immigrants and homeless.