Are you saying being nondenominational has little to do with theology? One pastor breaks off from another church because of polity, not theology?
It depends. In the case of my church, we were started as a Pentecostal Church of God (which is a denomination very similar to the Assemblies of God). From what my family tells me (this all happened before I was born), our church always had problems. Our pastors were always making the congregation mad, and the congregation actually starved out some of the ministers. Anytime a pastor made the church mad, a group of church members would leave church and walk next door to a member’s house and call the district (the middle judicatory between the local church and the General Convention). Then the district would have to send someone down from Virginia to settle the petty disputes in our congregation. I’ve been told that when our church left the PCG they were just about to kick us out anyway.
So we left, but it was never about theology. We all agreed on doctrine, but we could never get along with the pastors. Eventually, my church’s last PCG pastor left to pastor another PCG, and my church elected a young man who had been called to preach but was not licensed by the PCG. So, he became our pastor and we left the PCG. He is still our pastor today decades later, probably because he understands the dynamics of our church unlike the pastors that we got from the PCG.
I suppose whether splitting off from a larger group would be considered a theological question varies by tradition. In the Pentecostal tradition, congregational independence is highly valued. Churches join denominations because there are benefits in cooperating with other churches. You get combined resources for missionary work and church planting, you get ecclessiastical oversight and discipline. However, cooperation can come in many forms and there is no theological imperative to swear allegiance to the Pentecostal Church of God or any other church. My church still cooperates with other churches and ministries, but it is on a voluntary basis now. We’re not required to cooperate with another church or agency just because we share the same denomination.
However, if there was a Catholic church or an Episcopal church that decided to go non-denominational I supppose that definitely would be a theological controversy. But for Pentecostals and Baptists (which practice congregational autonomy) and similar traditions, a local church going non-denominational is not unusual. For that matter, an independent Pentecostal or Baptist church deciding to join a Pentecostal or Baptist denomination also happens.