Not really; religious identity politics are often used by leaders (whose motivation seems to be more power-seeking than genuinely religious) to connect with foot-soldiers (whose real impetus seems often to be desperation to improve conditions for their family, or themselves, or to redress wrongs they feel have been done to their family or themselves, or to feel connected to a group and gain meaning.)
And you see the same thing done in other places with racial identity politics, economic class identity politics, national identity politics, etc. (And, in many cases, many of these are at play in the same movement.)
Desperation, poverty, redress of (centuries long) wrongs, and seeing no other option than to join the movement do make sense as motives though.
I haven't studied all of those wars, but my understanding has been that behind every religious explanation for war is a political power struggle.
Religion is used to get ordinary people to go to war, certainly. If it wasn't religion, it would be something else that speaks to people's emotions and desire to belong to a group. (Patriotism, 'Duty', 'Honor', etc.)
For two of your examples:
The crusades cemented the power of the Papacy and Holy Roman Empire in Europe, partly by sending a lot of armed powerful people to fight elsewhere. It also was an attempt to reunite Catholicism under the Roman Pope (i.e. it was a massive land/tax/power grab by the Pope at the time). Fighting other faiths occurred, and was certainly used as a reason for people to leave their homes and travel hundreds of miles to fight foreigners. (I'm pretty convinced very few people do that willingly.)
The whole Protestant reformation taking off at all (Luther was not the first person to rail against the perceived hypocrisies of the Catholic church) and subsequent 30 years war was generally driven by a desire of the various princes and kings involved to remove themselves from Catholicism. The 30 years war also quickly devolved past Protestants vs. Catholics and largely into various factions jostling for power.
Everyone has an existential crisis in their life, and desires to become a part of something greater than themselves.
The traditional institutions in Western society that promoted this sense of belonging have been eroded in the recent decade, which could explain the trend toward joining organizations like ISIS and their ilk.
At the larger scale, religious justifications are no more relevant than socialism's role in turning some rural Cambodians into ruthless killers (as opposed to the state-terrorism): http://johnpilger.com/articles/from-pol-pot-to-isis-anything...
It is like Steven Weinberg summarized: With or without [religion] you would have good people doing good things and evil people doing evil things. But for good people to do evil things, that takes religion.
Recognizing this is important for assessing the situation and how to counter the problem – this is not a circumstance where more mental health services will make the tiniest difference. It requires intelligent debate about education, philosophy (including religion), and how to convey to people that any religious beliefs that cause the deaths of others are simply wrong.
Religion is not per se horrible – obviously the super-majority of religious people are fully functional contributing members of society and should be protected just like everyone else - but it has been used throughout history to conduct a huge number of atrocities.