Christianity

Let's make one thing straight from the start, so there wont be any misunderstandings after. I have nothing against any kind of religion, nor am I in favor of one. So this is not meant to insult or offend anyone, these are nearly my thoughts going wild about this issue...
This question's been bugging me for awhile now... well not just this one...but this one is the most interesting... so... what I want to write about here is some aspects of church...actually I wanna post this question...and see what you all think of it... sure it might be a bit naive to ask something like this... because I already know how things go...but hear me out...
so, let's take catholic church and orthodox church... they both belong to Christianity ...so my question is... how come (or correct me if I'm wrong) people- well lets be more specific, a man from orthodox church can't marry a woman from catholic church? Considering the fact that they both believe in the same God, in front of whom they're suposed to get married! It would make sense that people belonging to the same religion - Christianity should be able to get married in front of that same God... no matter what church they belong to... or do we have different Gods in Christianity?