Atheism is most certainly an ideology.
There are six schools of thought within Hinduism addressed as the Shat (Astik) Darshana (darshana meaning "viewpoint.") Within the Astika schools of Hindu philosophy, the Samkhya and the early Mimamsa school did not accept a God in their respective systems.
The atheistic viewpoint as present in the Samkhya and Mimamsa schools of Hindu philosophy takes the form of rejecting a creator-God. The Samkhya school believed in a dual existence of Prakriti ("nature") and Purusha ("spirit") and had no place for an Ishvara ("God") in its system. The early Mimamsakas believed in a adrishta ("unseen") that was the result of performing karmas ("works") and saw no need for an Ishvara in their system. Mimamsa, as a philosophy, deals exclusively with karma and thus is sometimes called Karma-Mimamsa.