"What is that religious movement?"
Translation:Quel est ce mouvement religieux ?
As est ce is an inversion of c'est it needs to be hyphenated. Having said that qu'est-ce doesn't really make much sense - it is like asking "What is religious movement?"
Quel is an adjective so, when a question is about a noun, it's a good bet that quel (or one of its variants) will be used. Quel is placed either directly before a noun or the conjugated form of the verb "être ".