The bible speaks of many important truths. Core gospel truths (such as the virgin birth, the substitutionary atonement, the resurrection) are worth dying for. As followers of Jesus Christ, there is no room for agreeing-to-disagree on these issues.
The bible also speaks about other important issues that are secondary to the gospel. These issues (such as baptism, spiritual gifts, the church in general) are serious ones and should be discussed. Despite their importance, these issues are not worth dying for. In fact, they are not worth dividing over either. We know this because the bible never tells us to divide from other Christians. The dividing line is the gospel (Galatians 1:6-9).
As Christians, when we are discussing secondary issues, we should agree-to-disagree when we cannot come to a resolution. There is absolutely nothing wrong with this. In fact, it shows both unity and humility.
I have heard the idea of agreeing-to-disagree criticized by some Christians. I believe they view this as theological compromise. I disagree.
Part of the problem is a misunderstanding over what agreeing-to-disagree actually means. On the positive side, it means that Christians can remain united while disagreeing over important issues.
On the flip side of the coin, below are five things that agreeing-to-disagree does not mean:
1. The issue isn't important to you. Just because you remain united with someone who disagrees with you, this does not mean that the issue isn't important to you. For example, I strongly believe that only believers in Christ should be baptized. Despite this, I'm not going to divide from those who hold to infant baptism.
2. You don't care about the issue. This is closely related to number 1. You may care deeply about it. Agreeing-to-disagree does not show apathy. It does not equal compromise.
3. All ideas are relative. Some people will say that everything is relative and that truth doesn't matter and/or exist. When you agree-to-disagree, you are not saying this. You are not caving on the truth by remaining united with those you disagree with.
4. There is no absolute truth. This is, obviously, closely related to number 3. In our postmodern society it is fashionable to insist that, especially in religious matters, absolute truth is nonexistent. That is simply not what you are implying when you agree-to-disagree.
5. You don't hold strong convictions. This is one of the primary charges against those who don't divide over secondary doctrines. It is simply false. You may hold very strong convictions about these doctrines. When you agree-to-disagree, you are also showing that you hold strong convictions about the doctrine of the unity of the church. Those who divide over secondary doctrines cannot say the same of themselves.
I strongly encourage you to think about what doctrines/issues are worth dividing over. In other words, what issues does the bible instruct us to divide over? The bible tells us that it is the gospel and the gospel alone. In light of this, we must ask why denominations even exist. We know that Christ prayed for His church to be united. He never prayed for denominations.
When you desire to remain united with brothers and sisters in Christ, you will have to sometimes agree-to-disagree. When you do this, you show both humility and unity. Also, you are not caving on the truth or implying that you don't have strong convictions.
Hold to the truth. Know what you believe. Unite with other Christians. Be humble. Be willing to agree-to-disagree.