There are two main problems, with regards to Christian Unity - one is that those who follow the apple, thinking it's a tomato get considered followers of the One True Tomato, either as people only have a vague idea of what a tomato is, or because they don't question enough and go "sounds like a tomato to me". The other problem are those who refuse to unite around the fact that they follow the same thing - the One True Tomato, and make mountains over minor issues (obviously they haven't heard the famous song!).
There also is a third problem, one that's really obviously stupid, but still gets done lots - that's when people think that the banana and the tomato are the same thing, simply as some people call the banana a tomato. This means that obviously there should be fellowship between both groups, as they say and think that follow the tomato.
A Catholic friend of mine wanted unity over the fact that we are both Christians. I gave him the benefit of the doubt, but explained that Catholic official doctrine isn't Christian, and that while there are some Christians in the Roman Catholic Church, the RCC itself isn't Christian. He then explained that "Through Jesus, and the intervention of His mother, and my own patron saint's intervention on my behalf I might stand a chance of redemtion." and that therefore, he's a Christian. I then explained that if Jesus needs the help of Mary and of a saint to intercede to the Father (who loves the Son), then he's rather rubbish - basically God's not good enough to do it on His own in my friends view. It's a different god, a different Christ - it's an apple, not a tomato. (I also put his 'might stand a chance' against the Hebrews 11:1 definition of faith, and found it lacking, and suggested that he might like to read Romans 8, Ephesians 1 and other texts that show that assurance is there for Christians and his complete lack of any form of assurance shows that he's not a Christian at all).
Likewise, it's like that with the whole gay Bishops Anglican split. Parts of the Anglican communion in the USA, Canada and the UK have changed track and started chasing an apple, rather than that tomato. The apple of a god whose changed his mind, a god who says "homosexuality isn't a sin - I know I made it rather clear in my book 2000 years ago that it was, but it's not now". Many, many people are deceived that this apple is a tomato, even if they disagree with what's been said, they're treating it as a pronunciation difference, rather than a whole separate fruit, but at the base of it, it's a god that flip flops, one that you can't trust his promises, because he might change his mind - that's not the God who revealed himself in the Bible, who calls us to trust him and remember his faithfulness to his promises as the basis of the whole of our response (there's more, but it all stems from that trust). It's a different fruit - there can't be unity there.
To sum up - if it's the same God, go for unity and fellowship despite disagreements on what are minor issues. If it's not the same God, don't. People who aren't Christian have exchanged the truth of God for a lie - they worship created things, rather than God himself - even if they look like God from a distance and on the surface. While we can (and should) dialogue with those who worship a different god, we shouldn't have any false pretences that they are worshipping the same God, or that they are Christian - for they have a different Christ, one who can't save.