Should I date someone whose theology is different?

Don't ask the minimalistic question. If you only want to know how little you have to agree on together in order to move forward, then you're asking the wrong question.

There should be a robust and common enthusiasm and joy about the gospel. You should also have a similar understanding of the gospel so that you're not always tricking each other by your words. You want to make sure that you have the same definitions for the words that you use.

So start at the center, and want the most.

It is difficult to rear your children and to worship together if you disagree on the center of the gospel and on the big issues of God's sovereignty. This involves the centrality of the cross, the substitutionary atonement, the inerrancy of the Scriptures, and the role of God in sin and suffering. You have to be able to nurture each other in ways that don't offend the other, and that flows from your view of the sovereignty of God.

So if one of you believes that God is not sovereign over the troubles of your life and over the salvation of the lost, but the other one does, then it is going to be very difficult for you in worship, devotion, and child rearing.

I would be very hesitant, frankly, to move forward in a relationship where there are deeply rooted differences about God's sovereignty, the gospel, or the inerrancy of Scripture. In regards to more marginal things, however, I wouldn't make them a criteria.