They had a larger population after they'd already conquered gigantic swathes of Christian lands, yes... not before that. And while they were obviously still fighting on occasion with the Christians or trying to take over certain parts of Christian territory, I think we can agree the big wave of conquest ended a long time before the Mongols.
As for the Crusades, what you say is true as far as it goes, but ignores that the Muslims were hardly a monolithic community anymore by that point (to the extent they ever were), and the ones living in the Holy Land really weren't responsible for the aggressive attacks of the Seljuk Turks (who at that point had been Muslims for how long, half a century? if that?) against the Byzantines. In any case the Crusades weren't exactly a purely religious war - one can blame the Papacy for encouraging them, but at the end of the day the western Crusaders also attacked and murdered Byzantine Christians and Holy Land Christians, seeming to view them as little better than Muslims. And in the Holy Land during the Crusades, the same thing happened as what happened in any region where Muslims and Christians coexisted for any moderately long period of time, like Spain or the Byzantine heartlands: alliances were made across religious boundaries as the political situation required, and it was normal enough for Christians to join Muslims in a fight against other Christians, or the other way around.