No Neolithic person left a statement of belief, so every religious claim about the period is read off objects. That is worth saying at the front of any account, because Neolithic religion has attracted more confident reconstruction than almost any other subject in prehistory. Figurines have been interpreted as goddesses, as toys, as portraits and as teaching aids; burials have been read as ancestor cult, as status display and as practical disposal; alignments have been read as calendars, as theology and as coincidence.
Bioarchaeological work at Catalhoyuk by Clark Spencer Larsen and colleagues shows what a rigorous approach can actually establish, which is a great deal about health, diet, mobility and labour, and rather less about what anyone thought. The period is also not a period in the ordinary sense. It is defined by a way of living, farming with polished stone tools and without metal, so it begins and ends thousands of years apart in different regions, and a date range for it is only meaningful once a region is specified. The atlas gives a wide range and says so plainly, rather than implying a single global era with a single religion in it. What is catalogued under the Neolithic here should be read the same way: they are contemporaneous only in the loosest sense, and a monument in Anatolia and a monument in Orkney belong to societies that had no contact with each other and no reason to think alike.