Without seeing your articles, we can only guess. My guess is that you don't bring anything new and exciting to the table. I am an atheist and will be one as long as I can think rationally (and when that stops, I don't think that person is "me" anymore, since my rationality is central to my persona).
But when I read atheists, I hear the same old arguments, and editors don't want to publish recycled opinions everybody has already heard, especially when about 85% of their audience (in the USA) won't read the article at all!
Contrary to George Costanza on Seinfeld, people will not watch a show "because its on TV", and they won't read an article just because it is in a magazine.
Your pitch may make the editor think he likes the topic if you can bring him something fresh, and then gets your article and its blandly argued, generic, and nothing special. So you lose to something special, and very special, because most editors will have a backlog of good "evergreen" articles they could choose to publish (evergreen writing is not tied to current events or anticipating new events).
I would read the magazines you cannot get into, and look for non-staff writers, and see what they did. Try to find some that don't seem to have particular credentials (usually they will list credentials in a sidebar, otherwise google the name).
My comment above reads:
You become qualified to write about atheism with credentials (e.g. a doctorate in philosophy, published academic articles), or by being becoming famous by some other route (Ron Reagan, famous as Ronald Reagan's son, is also an unabashed atheist).
Stephen Hawking, Steven Pinker, Richard Dawkins are all famous academics in other scientific fields. Sam Harris is a PhD in cognitive neuro-science.
People (and editors) trust Name recognition (Ron Reagan, celebrities of screen, sports, music) and indisputable credentials (PhDs with real scientific publications). Combined with laymen-readable writing.
Find somebody without any of those credentials, and chances are they have done something clever, or their writing shines particularly well. The editor chose them for some reason, so don't dismiss them by saying your writing is just as good, it isn't! Face reality and try to learn something from them. Steal their style. Match their word count. Make as many rhetorical points as they do.
If you can't find any author of any article that isn't an employee and isn't famous for some reason or well credentialed, then that is likely the magazine isn't interested in you. Most are intended to be profit machines, not public servants, and there is no profit in devoting a page to something that isn't going to be read. Depending upon their print run, they get thousands of $ for a full page ad there instead, or they can pick some fun evergreen article instead.
You need to do something new and interesting. Presuming you are a decent writer, failure to do that is the #1 reason for rejection.