A good place to start is with the Greek word for tolerance which is "anechomai". This word means, "to put up with, endure, or to bear with someone" and is used in several places including Ephesians 4:2 and Colossians 3:13. Ephesians 4:2 says we should tolerate each other in love as we are living our lives in a manner worthy of Christ. We are not to just "put up with" or "bear with" each other, but we are to do this in love. We do not have to agree on everything. On the contrary, by the very definition of the Greek word, we do not agree, but we put up with the person, in love, for the sake of unity. We would not have to tolerate them if we agreed.
Let us look at an example of how we should deal with the poor. Maybe you lay out a case from scripture that shows that the poor were taken care of by government rules (ie. gleaning) and therefore, you are for some sort of government intervention in helping the poor. On the other side, maybe you show from scripture that it is the church's job to take care of the poor and therefore, you are for private non-profits and church's helping the poor. Are either of these positions so far out that we cannot tolerate each other? Do they break down Christ's message? I would say no. Can and should we have strong beliefs based on the Bible? Yes. Should we tolerate others that have different beliefs than we do? I would say yes.
Let's clarify a little more about tolerance. The Bible advocates toleration of people not toleration of ideas. We are to tolerate, put up with, bear with people, not ideas. We can agree to tolerate each other and still strongly disagree in love. We can hold our convictions on issues and politics while tolerating each other and all the while having unity in Christ (if your beliefs are within orthodoxy). The media seems to push toleration of ideas which means that in order to have toleration for someone we must agree with them. This is not what the Bible is talking about. You can still disagree and have toleration for someone.
Toleration is needed for Christian unity. Can Christians have unity even though they are a republican or a democrat? Are we about how much government we should or should not have in our lives? I would say that we should be about Christ! We can have differing opinions based on scripture and still tolerate each other. However, many times we draw the line in the sand over issues that are not central to our faith or unity.
As Christians there are some convictions that are central to our unity. Among these convictions are the identity and nature of God, our sinful nature, and the way we are forgiven and accepted. Another thing that I think is very important for Christians is that we see holiness as God does, and agree with Him and the Bible on His standard. If you do not have these beliefs, then we can tolerate you and may agree with you politically, but we do not have unity in Christ with you. These convictions and beliefs, along with toleration of smaller points of difference, are what bring us to have unity in Christ.
In short, while we need to have toleration for each other on issues that are not central to our faith, there are still standards on what make us brothers and sister in Christ. Furthermore, having different standards and beliefs are not contrary to loving someone in Christ. We should have convictions based on scripture, while tolerating Christians that have different opinions on issues that are not central to faith in Christ.