No. The word ‘atheism’ never needs to be written with a capital letter (except in the cases where any word is – such as at the start of a sentence).
Words like ‘Christianity’, ‘Judaism’, and ‘Islam’ are always written with capital letters because they are proper nouns – much like names of countries, cities, or people.
The word ‘atheism’ is not a proper noun – it’s just a regular noun. It’s not the name of an organised group or a particular culture or tradition. It simply refers to a single philosophical position and concept. The most comparable words to it are words like ‘monotheism’ (the belief in a single god) and ‘polytheism’ (the belief in multiple gods), neither of which are generally capitalised.