JEDDAH, Saudi Arabia—Saudi women today are wearing clothes that, a few years ago, could have landed them in trouble with the police.

Many are abandoning the plain black version of the traditional abaya, a loose, body-covering dress that all Saudi women wear in public over their clothing to comply with decency laws. In its place, they are opting for conservative but creative alternatives: sporty jumpsuits, business-cut robes and even kimonos.

The...