To take a step back, Satanism is a name given to those who worship or venerate the Devil of Abrahamic religions.
Atheistic Satanism is a refinement of that idea. We are atheists (or non-theists) who don’t believe in supernatural gods or devils. Instead, we practice what Per Faxneld described as;
…a system in which Satan is celebrated in a prominent position.
Is it a religion? Yes it is. Religions do not have to rely on the supernatural, theist element. Many large world religions are, or can be, non-theistic or practised in a non-theistic way including Buddhism, Taoism, Hinduism and Jainism. Even Christianity has an atheistic/non-theistic sect.
Within Atheistic Satanism there is a further division. There is the old style, traditional LaVeyan Satanism and pseudo-LaVeyan Satanism as practiced by the Church of Satan and The Satanic Temple. These are ostensibly right-wing organisations, or in the case of The Satanic Temple, led by right-wing individuals.
Then there are groups like us belonging to a movement we loosely refer to as Modern Atheistic Satanism. We are much more progressive than the traditional LaVeyan groups and we see our roots as coming from the Satan figure of John Milton’s epic poem of the 17th Century, ‘Paradise Lost’ as interpreted by pre-Enlightenment and Enlightenment writers and political thinkers such as William Godwin, Mary Wollstonecraft, William Blake, Percy Shelley, George Gordon Byron, George Sand, Jules Michlet, Henry M Tichenor, Felix Pignal, Giosuè Carducci, Mikhail Bakunin, Pierre-Joseph Proudhon and others.
They were either inspirers of, part of or inspired by Romantic Satanism, a contemporaneous movement that eschewed the medieval, supernatural basis of Milton’s Satan and highlighted his intelligent, well-reasoned refusal to obey arbitrary authority. For more on this subject, see the suggested reading list page.