Are you serious?!

It was the main reason why I stopped playing Civ4 after a game or two. The impact that religion had on the trade system spoiled every fun in playing that game. The trade system in Civ4 was already very "limited", e.g. it was not possible to buy/sell techs for resources etc. etc...
And then, when your neighbor happened to establish a religion different from yours, he stopped trading with you completely! How much fun is that? Trading has always been an integral part of Civilization for me, from Civ1 through Civ3. Technologies, Maps, Resources, Contacts, Workers, Gold, Pacts and Alliances, etc. And in Civ4 that was possible only in a very limited way and then at some point no longer possible at all. That killed the game for me.
And honestly: how realistic is that? In "real life" trade relations between Occident and Orient have been established since Marco Polo's times, and probably even before that. Religion has never been a hindrance when it comes to making business... Not even in the Thirty Years War, which supposedly was about Religion: France (katholic) lead war against Austria (katholic) and during that time had alliances with Sweden (protestantic) and the Osman Empire (Muslimic)... Don't tell me that different Religion is always a hindrance for good relations...
And today? Arabia is selling Oil for big bucks to all the (Christian) western nations and China is selling about everything to the western nations... And here we not only have different Religions but also different political systems on top of that...
So in short: for me, the way Religion was implemented in Civ4 was the worst thing that ever happened to the Civ series.