TLDR: Atheism wasn't really regarded as a threat (other than the thing that USSR enforced) until the aughts and the New Atheism movement, at which point right-wing religious ministries turned from hating on other ministries to hating on atheists and secularists.

Atheism has some fascinating recent history. In the 1970s and 1980s atheists were disregarded almost entirely since it was an asserted position mostly by hard-line scientists and philosophers. Most of the none population instead went to (or at least associated with) left-wing churches. My parents (my Dad who is a rocket scientist and was atheist except in name) joined my mom and I at the Church of Religious Science (later the Science of Mind Church) which is pretty darned lax and easy to accept as religions go.

And the religious right (then, the Southern Baptist Church and the rising Evangelical movement) hated us and declared us false. They also did this to the Church of Jesus Christ of Latter Day Saints (still regarded as a dangerous cult) and the Roman Catholic Church. John F. Kennedy got a lot of flack for being Catholic, and Republicans insisted he'd be beholden to the Holy See -- and they tried to pressure him! -- but he demonstrated he could serve the US as president and keep the Vatican at arm's reach. Romney was still getting crap for his Mormonism in his 2012 presidential run, but it blended seamlessly into all sorts of other biographical anomalies that suggested character problems.

I should add there was a pro-religion sentiment in the US that was really anti-USSR. Marx recognized religion as the opiate of the people a symptom that the masses were suffering from precarity or scarcity, but Marx was saying the response of the community should be to feed them and keep them free of want, and as the dispair fades the need for religious practice will fade as well. (We're not sure if he's completely right.) So Lenin and Stalin's response was to ban religion, which didn't actually address the issue, but it gave the US justification to push church-going in the mid 20th century as a thing that pinko commies didn't do.

Anyway, atheism became significant movement thing due to two factors. One was the new atheist movement which orbited Richard Dawkins and the top atheist guns. Dawkins motivation (as he tells it) was the 9/11 attacks, which showcased the power of religion as a force multiplier in violent conflict. But there was also a certain privilege that religious movements and religious institutions were given that secular ones were not, which was a favored topic of Douglas Adams. And so bringing atheist and secular organizations to equal status as churches was a big early goal of the new atheist movement.

The other factor bringing the rise of popular atheism was the rise of the internet which allowed us all to actually talk about things and confront that a lot of us already had awkward relationships with our respective religious institutions. Myself, this was a period for me to naturalism, ruling out supernatural elements until one comes and bites me on the butt. (This is the dream for IRL ghost hunters, to have a poltergeist beat them with their own duffel. Pain is temporary but evidence lives forever on the internet!)

That said the aughts marked the spread of atheism (and the consequential collapse of left-wing church attendance. Right wing church attendance has been falling less quickly but noticeably, and ministries continue to be in panic about it. And this was when anti-atheist pro-Christian and pro-Muslim movements (who absolutely don't ally) started organizing to scare everyone how terrible we godless folk are, as if our interest in intellectual exercise and not the hypocrisy endemic to right-wing Christian ministries is what is driving parishioners from their pews.

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