We see some traces or left over signs of religion and "holiness". What are these? Why have they become forbidden? What does it mean that some still secretly practice signs despite them being illegal or forbidden?

In the novel, society is ruled by a global government.... religion is not welcome. None-the-less, Ender's parents have not given up their religion; his mother is Mormon, and his father is Roman Catholic. Ender's father even had him baptized secretly.... and all three children have names with religious connotations. Andrew (Ender) is named for the apostle, as is Peter, whereas Valentine is named for a saint.