I've dated this woman for a while. She wasn't super religious but she did go to church on Sundays once or twice a month. She was clear on the fact that I was not religious and we never had an argument regarding this topic.
I believe relationships require compromise and support from both sides. So some Sundays while she went to church, I would go ride my bike on some trails (impossible to do this together)
But once in a while, I would go to church with her, and sat (or stood) respectfully thru mass. She knew I was doing this for her, to show respect for her beliefs and to be able to share something that was important to her.
On the same token, she would give me space to do things I was into but she wasn't, and once in a while, she would make an effort to participate in some of these, like taking a bike ride or going to a rock concert with me.
I think the bottom line is, that if both people respect each other and their beliefs, there is no reason the relationship should fall apart because of this. Now if one of the parties insists in trying to change the other's mind, well the problem is not religion, the problem is that person's lack of consideration and respect for who they are dating...and who wants to date someone like that anyway?

I say see where things go. To just drop someone because of their belief system seems a bit harsh. This person would also have to accept my beliefs without judgements. But finding someone open-minded enough to live with such differences is the hard part.