Every atheist (aside from the imaginary scenario of an orphan being raised by a herd of buffalo in remote Africa or whatever) will provide, even if only to themselves, the means to refuse, refute, disbelieve or otherwise contextualize theistic ideology.
That's because the only way that one can confront, agree, critique or otherwise deal with an ideology is with an ideology. Trying to lump low end political advocates of an ideology with persons who are totally bereft of a knowledge base in the field is simply absurd
... although granted that the variations within an ideology are often categorized in regards to the political hue of the advocate.
I am not denying that anti-theism is a real term. What I am suggesting however is that you are wrong to suggest that only an anti-theist partakes of an ideological stance ..... much like it is wrong to suggest that it was only persons who took an active political stance to oust the British from Ireland (by joining the IRA for example) that partook of the ideology of Irish independence ... or that those who didn't express such a level of political involvement are ideologically on par with new born babies in china (since new born babies in china also have a politically neutral attitude to British involvement in Irish politics)