A man should use the same criteria whether she is a BT or FFB or a Convert. If he a really feels that he needs a B’sulah or someone with good Midos or from a good family etc, then if a BT or convert also has his qualifications why would he not be interested!!!!!!
A diamond is a diamond, no matter where it is found.
In Business they say “Location, Location, Location”
In Shaduchim they should say “Midos, Midos, Midos”