Their paranoid reason for refusal says more about them than about you.
When I was growing up in Boro Park, over a period of twenty years, my parents rented the basement to an assortment of odd characters including a divorced woman with a baby, a single Ger/Baal Teshuva (He wasn’t sure if he was born Jewish) and a 20 y/o OTD kid who smoked marijuana with his hippie friends. For the most part they paid their rent on time and we never had the slightest problem relating to them ‘preying’ on anyone.