Atheist is literally “not theist” which would include nothing, none, agnostic (the belief that it’s impossible to determine the existence or absence of, in this context, God). It could even be argued that people who believe in God but do not participate in theistic practices (eg lapsed Catholics) are atheists. It does not require or even imply some position against religion.
This isn’t accurate though. In the most semantic, etymological sense perhaps. But atheism is widely understood to be the disbelief in deities. Agnosticism and atheism are very different. One is a position of belief (I cannot prove god doesn’t exist, but I don’t believe it to be so) and one is a position of ignorance (I cannot prove god does exist or doesn’t exist). Words, meanings and definitions are defined by who is interpreting them. This therefore means that the definition is whatever the majority believes it to be. You may as well be looking at a field of flowers and describing them as gay. It may have been the appropriate term once, but it is not now. And we live now. The etymology of the term is not the same as the meaning of the term. Sitting there and prescribing that your interpretation of the term is the correct interpretation reminds me a lot of the tale of King cnut.
Atheism and Agonistism are under the umbrella of Irreligion or Non-Religious. They are seperate identies.