If they are not frum they can't be trusted
that's not true.
If they are mechalel shabbos befarheseia they lose their nemanus. (or avoda zara). as per the definition of mechalel shabbos befarhesia put forth by the MB and other achronim, almost all people who live in a frum community and are married to frum people don't qualify. (I know of one exception). Then there is inherent nemanus, unless of course you think they are lying. which obviously the frum spouse doesn't here.