You don't have to compete, simply defend the only way the AI can win
You'll need to compete to get the religion and keep it at the very least. And making that a priority in the early game on deity is not very efficient in order to win. It might be the easiest way to be sure to avoid losing, but I'll argue the easiest way of winning on deity is ignoring religion completely and risk the very slim chance of the AI winning a religious victory.