That is not what a religion is.
> Secular Americans are annoying because they believe they don't have one
Why is that a problem to you?
> and instead think they're just "good people", calling those who break their core values "bad people".
No, not really. Someone is not good or bad because you agree with them. Even a religious person can recognise that an atheist doing charitable work is being good, regardless of whether they share a specific set of belief.
The attitude you describe is wrong, and from my experience much more common in religious fundamentalists than radical atheists (the vast majority of people in western democracies do not care whether you have a religion). I have never seen an atheist saying that. But I’ve had priests telling me that I had not "rejected Satan" because I was not baptised.