I am a Baptist. I believe that the 1689 London Baptist Confession and the 1858 Abstract of Principles are faithful summations of Biblical teaching.
However, I am also arrogant about being a Baptist. For this, I apologize.
When I see a Methodist (or a Presbyterian, a Lutheran, a Pentecostal, etc.), what do I see? Instead of seeing a brother or sister in Christ, I tend to first see a person whose doctrinal beliefs are not as Biblical as what I consider mine to be. I focus on what makes us different instead of on what should bring us together: our faith in our Lord and Savior Jesus Christ.
I know as well as you do that some people who claim to be Methodists are not saved. However, the same is true for Baptists. In fact, the misapplied belief in "once saved, always saved" may even lead more Baptists than Methodists to falsely believe they are going to heaven even if their lives are bearing no fruit.
I know many people who are godly saints who also attend Methodist churches. So why do I first look to what separates instead of what unites? My only conclusion is that it makes me feel good to be right, and have others be wrong. This certainly does not please Christ.
So if I focus on unity, in what areas (practically speaking) can I be united with folks of other denominations (assuming they believe in Jesus as Lord and Savior)? The answer is simple: in almost every area. I can unite with them in missions and evangelism. I can unite with them in ministry work in the community. I can unite with them in prayer for revival in our community, state, and country. I can unite with them on taking a stand for Biblical authority on social issues. I can unite with them on apologetics-related issues. I can unite with them while participating in in-home Bible studies.
The one place I cannot unite with Methodists, Lutherans, etc. is in membership in a local church. This is mostly because of the key issue of believer's baptism. A church simply cannot have different definitions of what this ordinance means within one body.
However, division should not be my first thought when I see a person from another denomination. My first thought should be, "Hey, there is another follower of Jesus Christ. I'm going to go see how they are doing, and how I can serve them in the Lord."