So if religious organizations can be non-profit should atheist groups be considered as non-prophet organizations?
Why can't you? Anyone can set up a non-profit organization. What would be harder for an atheist group to prove is calling yourselves a church to gain non-profit status that way. Other than that, an atheist group could start a non-profit organization. You don't have to have a religious reason to form a non-profit. It's basically about tax exemptions and tax deductible donations.
I hope some day in the future that non profits are truly held accountable for proving they are not gaining profit or especially profit for a select few. I do not believe they should be based on religion or lack of one. I believe that non profits should be humanitarian efforts that help those in need or provide a something useful for everyone.
Religious organizations should only be considered for non-profit status if they don't advocate for a specific political party or candidate or a private industry for that matter. This includes rating systems that favor various individual entities. Should the NRA be considered non-profit? They should be allowed to issue general statements that support their own positions on civic matters, but not to the extent that they show obvious favoritism toward a specific political group, or candidate.