To what degree would you say that contemporary global conflicts are being driven by culture and tradition related to organized religion, rather than other factors?

As a thought experiment, if you were able to wave a magic wand and have all organized religion erased from the planet, do you think it would become easier or harder to resolve global conflicts that currently exist in the world? To what degree is this an underlying factor in how conflicts currently play out?

To be clear about the hypothetical, people are free to believe whatever they want. There are just no organized structures to facilitate those beliefs and form identities around.