For nine years, I was a Dr. Ornish-very-low-fat-diet vegetarian. I believed it was best for my health. I was then presented with better evidence and logic, and I converted to become a Dr. Atkins-very-low-carbohydrate omnivore. I believed Dr. Ornish, because I was sufficiently convinced of the truth of his diet to live it out; I converted, because I wanted to believe the truth, and I found the truth to be closer to Atkins then Ornish. That is how conversion happens in anything requiring belief, and action based on belief.
P.S. OTOH, when I switched from being a United Methodist to an LCMS Lutheran, I didn't "convert" at all, because my beliefs did not change: it was the UMC denomination that had changed, I wanted to be where Christ was, and I found Him in the Lutheran church. If I ever find Him elsewhere, I'll follow Him there as well.
It sounds like you did not “convert” at all. Your beliefs did not change with your change of denomination. I am the same way. My first church experience was with the Southern Baptists. When I got married I became a member of the Presbyterian Church (USA). When we had children we moved to a United Methodist Church in the town where we live. My core beliefs have not changed. I am sure that I differ with several principles of every denomination I have belonged to.