The ancient quarians practiced ancestor worship. Even after abandoning faith for secularism, quarians continued to revere the wisdom of elders. As time passed and technology advanced, they inevitably turned their knowledge to preserving the personalities and memories of the elderly as computer virtual intelligences. These recordings became a repository of knowledge and wisdom, stored in a central databank and available through any extranet connection.
They held no illusions that this was a form of immortality; like all virtual intelligences, their electronically-preserved ancestors were not truly sapient. This was considered a surmountable problem; sapience could surely be reduced to simple mathematics.
The quarians began exhaustive research into creating artificial intelligence to they could learn to escape the bounds of mortality and give their ancestral records true awareness. Unfortunately, the life the quarians created did not accept the same truths they did. The geth destroyed the ancestor databanks when they took over.
In the centuries they evacuated their homeworld, most quarians have returned to religion in various forms. Many believe that the rise of the geth and the destruction of their 'ancestors' were chastisement for arrogantly forsaking the old ways and venerating self-made idols.
Others have a more philosophical outlook, believing that their race was indeed arrogant, but no supernatural agency lay behind the geth revolt. Rather, the quarians' actions wrought their own doom. Either way, every quarian would agree that their own hubris cost them their homeworld.