There are an awful lot of people who use religion as an uncertainty reduction device.
Initially, the convert is providing to the local church he is converting to apparent confirmation of their beliefs. Look, they say, this guy showed up and converted because of the awesome inherent truthfulness of our church. But the convert moved from church A to church B because of a massive disruption in his certainty. He once, presumably, felt that church A had all the answers. Something occurred to destroy that certainty.
In many cases, the convert is also seeking to use the new religion as an uncertainty reduction device.
If he is not very interested in doctrine, maybe the new church will work for a while. If he knows anything, uncertainty will creep up on him again. He may begin to notice Christianity looks like many small flames in darkness, and the flames are not congregated around a particular denomination or authority structure. He may notice the brokenness of communion; the loss of place in this egalitarian and democratic age.
Meanwhile, he may find himself in conflict because he has actually read stuff, cared enough to go look at ecumenical councils, read the bible, maybe some Church fathers, and tried to follow certain ideas to their logical ends. It doesn't make for a comfortable fit in church A, and it won't make for a good fit in church B either.
The would be convert is, in a sense, a church unto himself. He is exercising his own judgement, which necessary subverts authority. How can the authority in church B find themselves comfortable with someone who once decided that his authorities in church A were wrong? Indeed, how hard is is exactly, to notice most authorities tend to behave within the same bureaucratic parameters?
I used to have a strong sense of obedience, but now I realize this is essentially a conservative reaction to uncertainty, and one with a strong tendency to destroy that which we hold dear. So I could see a convert, in the beginning anyway, trying very hard to conform, but his conversion itself was an act of non-conformity.
I do believe, beneath the dross of a century or so, we find a Christianity capable of handling converts. An anarchy of sorts, an apparent cacophony of voices, but an aristocracy of sorts too, for the voices that counted where the voices of those seeking perfection, seeking to be like Him.