I was one for many years.
I grant you that American Atheists pretty much required left-leaning views...they were pretty paranoid that they were going to get infiltrated by religionists. (Maybe they've loosened up since Madalyn Murray O'Hair died, I don't know.) FFRF's newsletter always seemed a bit left leaning as well.
But, there are pro-life atheists out there. Pew says it is 11%. Doris Gordon, the founder of Libertarians for Life was an atheist. All of her reasoning was 100% atheist, and she wrote extensively on the subject. There was an Atheists & Agnostics for Life organization back when I was in law school. Not sure it is active anymore. Secular ProLife may have replaced them. Their position: "We see abortion not as a culture war issue or as a religious issue but as a human rights issue." That is my position. And, I think arguing that way will have much better pro-life impact than arguing from a religious point of view.
Those who claim abortion is merely a religious issue are using that claim as a cop-out so that they don't have to think through the issue. Young humans are being killed. It may help to be religious to see that is wrong, but you don't have to be religious to see that is wrong.