Not sure it has anything to do with that. Christians seem obsessed with accountability mostly likely because some of them would go around in a murderous rampage without their god (I have met people who said they would kill their neighbors if their god had not commanded them to do so). I have said it before and I will say it again, for me the tangible lack of evidence to support the existence of the Christian deity (or any other for that matter) is what makes me an atheist not so idea of accountability. Society holds me accountable, my own conscience holds me accountable as do the people in my life. I don't need a Canaanite storm deity to that for me.
'Spiritual' people are just people who haven't thought much about such things; it doesn't mean anything when they say the word.
I'd hardly call that "obsessed". As the saying goes, when the cat's away, the mice will play. We saw that, for example, when Moses left the Israelites for nearly a month and a half. They're barely out of Egypt, after praying for CENTURIES to be delivered; yet they revert right back to their heathen ways.
As for your claim of society holding you accountable, that comes, in no small part, because those in society will also be held accountable for their actions (or lack thereof).
As the risk of inaccurately speaking for Loco, he and I stated what we did, because the whole "spiritual not religious" routine is often just a talking PC point for nominally recognizing there's a God, provided they don't have to answer to Him or abide by any regulations that go contrary to their philosophical, political, emotional, or even physical inclinations (or, in Biblical laymen's terms, their flesh).