There are a lot of immersion breakers in the game. The very first (that has a religious background and semi relative to this thread and my first personal choice) is for example the Hagia Sophia. All wonders in the game are represented as they were during their construction but said wonder has both the Cross missing atop it and it has the minarates that were build roughly 1100 years after its construction by the Ottomans. Another one is the Parthenon, what are the roman legions doing there? Athens was a protectorate and the Roman legions never entered Athens in force. The garrison was outside the city in recognition of Athens as the cultural ancestry/precedence of Rome.
Anyway this is most probably the biggest immersion breaker -->
TLDR: Immersion is a whole other matter and simply put, the game doesn't have enough religions as it is to support all civs. More-so, when every civ has a chance to found a religion of its won you are running of 'immersive' options no matter what.
May I ask what is the symbol you propose? I have never happened upon it before.