Good non-religious people exist, and bad religious people exist. Religion might help a lot of people stay good or become better, but lack of religion is almost never a plausible cause for badness.
Indeed. Religion or not is often not the issue.
Self-criticism, humility, ability to take a step back on one's own belief system with its intrinsic limits and issues are. Which is often harder for fundamentalists, whatever their base is.
Edit: what OP may have wanted to say is that « following a religion is a make-believe that also makes you believe what you do is good ». Which is not much more reassuring either (but an apt « mise en abyme » observation of what religion without a sane self-criticism can become)