The first question we should ask is, what is incompatibility?
When we say something is incompatible, it means that both variables did not march or incomparable.
Should incompatibility be a reason for a break up in marriage. Well, the answer is "NO". Biblically.
But its always good to case sensitively when chosen your life partner, because incompatibility brings disaster in marriage if not properly handled, incompatibility can make marriage uninteresting even as a Christian.
Incompatibility from it deepest meaning, means not having the same vision and ideology with a particular person eg, "An unbeliever marrying a believer(Christian) hmm!!!
So to me its always advisable, when you wants to marry, as believer marry a believer too, as unbeliever do the same but if at any point in time you find out that you made a mistake (interchanging both), break up is not the best option, accept your fate and ask God to help you.
Just know that two things are involved, if he/she did not convert you, you will convert he/she...."For two cannot work unless they agree"