One doesn't need "religion" to have a god.
I think the problem is restrictive religions, not the gods of those religions.
As in, it's the whole "this is the only right god!" preached from a pulpit and people accepting it as is, raising their children to believe the same.
There are people who believe in a god(s)/goddess(es) who raise their children to respect all religions. Who don't teach their kids "this is the only way" but that "this is what I believe, here's what else is available, it's up to you".
But that's the thing about people.
As human beings, we hate to be wrong. It's in our system.
So when we're raised to "know" that there's just "one" god and it's commandments are these exact things, when someone doesn't follow what that god (and his spokesmen, the preachers) tell us is the only right way to live, and do just fine, then that indicates that maybe, just maybe, we're wrong. Maybe our god isn't the only one, maybe his commandments aren't "necessary", maybe the spokesmen aren't speaking on his behalf that well, maybe there are more than one ways to live and do just fine.
And to people who do good because they're {Insert Religion Here} not because they're good people, that's a horrible idea. To a lot of people, it means that if there isn't a god that rewards doing good, then people will stop doing good.
Ofcourse, they don't "see" it when good people do good things even if they're not {Insert Religion Here} because that would upset the "fact" that they do good because they Are {Insert Religion Here}.