What are some thoughts on whether or not two should get married if they have come from different doctrinal backgrounds and are looking at going into the ministry?
First of all, there are a lot of things one should consider when thinking about the possibility of marriage. I would strongly urge you to seek some premarital counseling, even before becoming formally engaged.
The most important thing on which you must agree is that you each trust in the shed blood of Jesus for the forgiveness of your sins. You can’t have a Christian marriage if you aren’t Christians.
One of the most important issues is that of character. I am thinking of Proverbs here. Some people plan to marry someone that the Bible says we should not associate with (like someone with an uncontrolled temper).
Now, to the issue that you have raised. I think it can be a good thing that you have come from different backgrounds, so long as you are of one mind now. What would be devastating to a marriage and to a ministry is to have husband and wife divided over things that could easily split the church or ministry. It is very easy to temporarily sweep fundamental differences under the rug in the early stages of a relationship, but they have a way of coming into the open in time.
I think that my best advise to you would be to find a mature Christian whom you both trust, and ask him to meet with you both to pursue some potential difficulties. If your differences are not competitive, they may be complimentary.