Although I realise it is unhelpful to the original request (for which I have no useful input), I'm curious as to why atheist dwarfs cause a problem for a theist based fortress. If you want to have them all worshipping around some kind of alter, why not make the atheist's alter a library and have them perform scientific studies? Or similar to Ironfang's suggestion, why not go with an "untouchable" class. They can be used exclusively for butchering animals, tanning hides, carrying corpses, cleaning etc. You could even build a shanty town for them to live in (maybe forcing them to live above ground). This would not be without historical precedent.
The options seem endless and interesting, so I'm wondering what you have in mind that requires that every dwarf worships something. I'm also wondering what you are thinking of doing about dwarfs that worship non-god entities. Especially in worlds that still have mega-beasts, it is not unusual to have dwarfs worshipping them.
I'm mostly worried about atheist dwarves outnumbering the theistic ones.
As for what I'm planning, I normally just nickname all dwarves based on their deity (so a worshipper of the god of storms becomes the 'Stormlord', a servant of the god of fortresses gets called 'Fortress Priest'), then give them labors appropriate to their god. 'Tasks appropriate to their god' is defined as 'anything I need done, assigned to whatever god is closest to it'. So servants of the god of weather may be put in charge of the farms, followers of the god of earth become miners and stonecrafters, and worshippers of the god of victory enter the militia. I usually only spend starting points on items, to avoid skill/labor mismatches.
Every faction has its own portion of the fortress outfitted for their specific tasks, with a large customized temple to their deity in its center. If worshippers of new gods arrive, they too get their own section.
It's great fun having to adapt your strategy on the deities that are currently worshipped (hm, tons of people who worship the goddess of music... I better make some instruments and build a tavern to properly praise Her), and the temple-centric structures really help with giving your fortress character.
Non-god entities are handled the same as gods. Dwarves show up worshipping a dragon? Better make a temple dedicated to the concepts of Fire and Wealth, meaning lots of gold and ornamental magma basins. The dwarves themselves could get jobs at forges or jeweler's workshops.
Okay, just thought of a great way to use the atheists; I'll have them serve Armok himself. Easy!