At best, a wash, likely worse. First, I think a number of things that get blamed on religion are probably best blamed on organized religion and not religion itself, and thus are largely due to the nature of any such things risen to that level of organization, which results in corruption and greed. Second, of those things that aren’t due to organized religion, they’re still usually due to human nature in some form and religion is used as justification. But most importantly, religion does serve several useful purposes.
Part of the problem with this sort of question is that even if we take that there is no god as a given, it doesn’t eliminate religion at all, because there are more than a few religions that don’t posit the existence of a god. At its core, religion is just a subset of philosophies that usually include things like moral behavior, purpose, and usually include belief systems and mythologies, etc. At best, you would eliminate the rituals and mythologies, but you would still have disagreements about other aspects as you do with any philosophy that attempts to define morality and purpose and such. More likely, you’d still have people using those philosophies to commit atrocities just as plenty of non-religious philosophies have been used as justifications.
So, you’d likely gain little or nothing, because human nature would still be human nature, but you’d lose the other less tangible aspects that religion brings along, particularly in the way of the arts and community. There are enormous bodies of work that are wholly or partially inspired by religions, and without religion, who knows what might have happened. And while, even as a theist myself, I’m generally against most rites, I think religious gathers focused on learning and studying those philosophical concepts and regular prayer/meditation are ultimately beneficial to all involved and their communities.
Either way, the idea that eliminating religion would somehow remove irrationalities and all is just silly. Sure, there are bigots that use religion as justification for their actions, but that’s like saying if the political party you’re opposed to and think are evil assholes dissolved, that somehow those ideas that formed it would vanish with it. If religion never existed, we’d still have racists, homophobes, and any number of other ideas, they would just find other reasons. In fact, the most bigotted person I’ve met was an atheist.