Don't look down on people just because they're poorly dressed.
Literal
Shabby appearance [object-を] doing [just-because-からといって] people [object-を] despise [must-not-てはいけない].
貧相な ('shabby, poor-looking') is a na-adjective. 身なりをしている means 'to be dressed in a certain way' — a set expression using している for a maintained appearance. 軽べつ is a variant spelling of 軽蔑 using hiragana for the second character.