A - Thanks for asking. I think you understand part of the difficulty of not having an authority to solve doctrinal disagreements. I will be speaking in generalities to answer your question, so please remember that not every Protestant denomination or group functions the same. Some have hierarchies - such as Presbyterians, Lutherans, and Episcopalians - though none are as defined as the Catholic Church. Others have little, if any, hierarchy - such as non-denominational churches, Baptist, and Pentecostals.
For those groups with little, if any, authority - the decisions about doctrine and belief are ultimately left up to the believer. Hence, the Southern Baptist Convention has a statement of belief that says:
Each congregation operates under the Lordship of Christ through democratic processes. In such a congregation each member is responsible and accountable to Christ as Lord. Its scriptural officers are pastors and deacons.Therefore you join a Church that believes as you do. These churches then join organizations that share their belief systems. There is no central authority. When doctrinal differences arise, you either live with the differences or separate. This is why there are thousands of different Protestant denominations. Each group has something that divides them from others.
The line is less fine when doctrine is not quite as clear. But, many groups have a clear belief system that draws a firm line as well. But, this does not make things easy. For instance, even though the Anglican Church (Episcopalians are the US Anglicans) and the Evangelical Lutheran Church of America (ELCA) both have those that are made bishops and have leaders with some authority, it hasn't stopped differences from starting to divide their churches. The Anglicans are suffering quite a bit with how to handle openly homosexual priests and bishops. Some others have thrown down the gauntlet and many think it is only a matter of time before there is a split again.
Pray for Christian unity. But, not a false unity of holding hands and ignoring our differences, but a real unity in belief and beatitude.