Assuming we agree on the basics of Christian faith (for example, the Apostle's Creed, which almost all Bible-believing Christian denominations generally uphold), how can we live with our differences? There are many ways, but here are three principles I've found useful.
1) Always Remember We Have the Same Father
Whether we agree with each other or not, we have a basis for relationship. This was very helpful for me when I graduated from a conservative college and joined a missions team of Mennonites, Pentecostals, Southern Baptists, and others.
Make every effort to keep the unity of the Spirit through the bond of peace. There is one body and one Spirit, just as you were called to one hope when you were called; one Lord, one faith, one baptism; one God and Father of all, who is over all and through all and in all.
-From Ephesians 4
2) Each Person Answers to Their Master Individually
So we should remember they will be judged and rewarded by their Master who knows their struggles and faith much better than we do.
Who are you to judge someone else’s servant? To their own master servants stand or fall. And they will stand, for the Lord is able to make them stand.
3) Look First For the Good In Others
Human tendency is to look first for areas of disagreement and wrong, but among brothers and sisters it should not be our first impulse. The verse below has wider application, yes, but it is in the context of disagreements between sisters in the church, and reminds us not to get stuck on what peeves us but look at the bigger and better picture.
I plead with Euodia and I plead with Syntyche to be of the same mind in the Lord. Yes, and I ask you, my true companion, help these women...Finally, brothers and sisters, whatever is true, whatever is noble, whatever is right, whatever is pure, whatever is lovely, whatever is admirable—if anything is excellent or praiseworthy—think about such things.
-From Philippians 4
I hope these three principles are useful as you relate to your brothers and sisters in Christ. What other principles have you discovered for dealing with other Christians who rub you the wrong way?