If you mixed with people at all, your chances of survival in 1000AD europe without an understanding of religion would be nil.
As Art_in_FL says understanding local mores are essential.
Even today one guide book warns visitors to Indonesia with the cautionary tale of a traveller who a passerby saw hiding money in his sock, so promptly laid him out with a punch. The king is very highly respected and putting his picture next to the feet was a gross insult in an islamic country.
Saying you are a protestant in 1000AD and explaining that 'was a church that didn't follow the pope' would mean a fast journey to a fire. Trying to dig your way out with the modern day: 'I'm not really religious' would lead to the same result.
If you claimed to be a christian and they could see you didn't know the rules of the Catholic Church; well god knows what they'd make of that. It wouln't be good....
The Sock