Is a young man's jealousy over his fiancée riding public transportation—where men and women intermingle—considered appropriate jealousy?

"Gheerah" (protective jealousy) over Allah's sacred prohibitions is religiously required and is one of the requisites of faith. If it is based on mere suspicions, then it is misplaced jealousy. However, if it is based on a firm fact, then it is appropriate jealousy, while considering the girl's religiosity and character. If something contrary to Islamic law is proven, then she must be advised kindly, keeping in mind that she is a non-mahram (a woman one can marry).