Hi Kurizgoth, I think it's dependent on the mid-game moment where your people decide to be either church peeps, factory peeps or future peeps. This was the case with previous versions of the game.
But they didn't build the factory either, even as i had the lab. On the screenshot it's 2 tiles down and 1 tile to the left from the windmill.
From the description of the factory, it needs the market, which is pretty unlucky if it's a "luck" thing mid-game.
PS: Even as i had enough food they didn't build it =( and it's not the fault on my resources. had like 30 of each.