The biggest issue that divides most Protestants isn't theology or Scripture, but rather church governance.
At the most radical end of the spectrum, Mennonites, Baptists, and other Anabaptists believe there is authority ceded to any priest beyond that which the local congregation gives it. As such, they have no bishops or eccelesicatical authority - Baptists have "conventions" i.e. meetings were churches will voluntary associate, but that's it. Indeed even the famous "Southern Baptist Convention" only technically exists for three days year. If these groups want to hire or fire a pastor, for example, they place an ad in the paper to get a new one.
In contrast, Methodists have Bishops and dicoeses, and a person who (at least in theory) can reassign priests amongst churches at his will and discretion.
Presbyterians and Lutherans have Synods which can make binding rulings on their own members. There are competing synods which have come down on certain issues (e.g. the PCUSA tends to take more liberal stances on issues like gay marriage, abortion, and social issues, whereas the PCA is a much more evangelical, conservative "bible-based" one) but neither would suggest the other is "clearly going to hell"
And, of course, you have the Episcopalians, who are basically Catholics in everything but the Pope. They may stress their independence from Rome, but if you attend an Episcopal service, as a Catholic, you'll feel very much at home.
Now, it would be an error to say there are no doctrinal differences - Methodists are Arminian (meaning they believe that a person must choose to be saved) whereas Presbyeterians are Calvinstic (and believe that God already elected those whom He presdestined to saved.) Alternatively, Baptists would say that the communion elements are strictly symbolic, whereas a Lutheran might argue consubstantiation or transubstantion- but candidly, these are all minor issues for most modern day Protestants. When compared to "You are going to hell if you aren't saved by Jesus Christ," these things appear to most Protestants as minor points of mechanism - not life and death issues.
Primarily, Protestant identity stems from a reliance on personal interpretation of Scripture (and hence a rejection of Papal infallibaility, no matter how awesome Francis might be), and a stress on what a Protestant would probably call "orthodoxy" over against sacrementalism. But again, even these differences can be seen as outgrowths of a rejection of governance, moreso than theology.
Jesus is Lord? Check
Saved By Grace? Check
Trinitarian? Hypostatic Union? Jesus is Way Cool, Dude?
Check, Check, and Check.
Finally, understand that "personal interpretation" does gloss over a lot. Contracts are written to be as precise as possible, specifically to avoid differences of opinion over what a thing "means." To ask, "why should personal interpretation lead to differences?" is almost silly one regard.
As an example, think not of doctrine, but of politics. Even a simple statement like:
"Congress shall make no rule regarding the establishment of a religion, or prohibiting the free exercise thereof"
can have radically different interpretations. Is a student-led prayer coercion? Or is stopping that valedictorian prohibiting his free exercise thereof? What about people who think that drugs are part of a spiritual experience? That's why we have a Court - to officially interpret what those words mean - in the same way you have a Pope. That said, we also have people with strong opinions that guide that decision making. Is a Court less messy than the alternative? Sure. But last time I checked, nobody thought they were infalliable.
But, no American is saying we should have Sharia Law. Fundamentally, we can agree on the main points - that Jesus is Lord, that we are saved by Him, the Creeds, etc..., and still differ on shades of meaning and certain use cases. That's really all that divides us.