2 Corinthians 6:14
Be ye not unequally yoked together with unbelievers: for what fellowship hath righteousness with unrighteousness? and what communion hath light with darkness?
Preachers preach all the time about not entering into relationships with people who do not share the same belief as you. Many couples who do not have a common religion often times end up with a rift between them; however, some couples make it work.
What are your beliefs about being "unequally yoked" with another person? What if everything about them fit your standards, except for a common religion?
I will most definitely agree that a relationship with someone that is equally yoked is the overall best relationship you could dream for. As far as converting someone and bringing them into the church is a wonderful thing that everyone should work towards daily but, if the only reason you are doing this is because you want the relationship potential with this person then you would be actually going about it backwards and teaching the person you are converting to do it backwards as well. Now let me explain... Bringing someone before the Lord should be just that, a selfish motive of a relationship can't be good. Not to say that you shouldn't have a relationship with someone that you convert, but it shouldn't be the reason that you convert them. And if the person you are attempting to convert isn't purely sincere then they will be coming to church for you first and the Lord second. Clearly the Lord comes first over all other loves. But as far as having a relationship with someone of a different religion there can be many extremes of that. A Methodist and a Baptist more often than not share enough common beliefs between the two religions that I don't see it becoming a problem. But on the other extreme, a Catholic and a Buddhist would most likely clash into a power struggle over who's beliefs are right and wrong. This most likely wouldn't happen right away, but the closer two people become, they cannot truly become connected if they look down on one other which I have seen in the past.