It is the official belief of Bible Brain that there are true Christians in all denominations, but that there are no true denominations. I don't believe it is necessarily sinful to claim a denomination, but I myself will not, as it is my view that the Bible condemns them as divisive and carnal.
A serious question we all need to consider is, how many truths are there? The correct answer is one. There is one God, to whom we are united with one baptism, following one faith, laid down in one Bible. There aren't hundreds of gods. If we should change denomination, we don't necessarily need to get baptised again (though there is, of course, a little nuance there). There aren't multiple Christianities. Even the Bible, translated hundreds of times, presents (barring corruption) the identical faith across all of them. Thus, if Christianity is true, there should be no denominations.
Yet, obviously there are, which brings us to question 2: why? If there is one truth, why are there so many denominations of it? The answer to that is twofold. First, let's be honest: There are some denominations that are just genuinely bad. Denominations that hold their doctrines even in spite of Scripture. That doesn't necessarily mean there are no true Christians who identify with that denomination, but that the denomination itself cannot possibly be Christian, and its members will ultimately have to choose between their denomination and their Christianity.
But note what Paul says about divisions. He says "I fed you with milk", because "you were not able to receive it (...), for you are still carnal". What does this mean? Put simply, we're all still human. Without going into too much depth about the specific errors of the Corinthian Church, they were by no means spiritually mature. Paul "fed them with milk", because they weren't ready for the meat. The Corinthians were saved, yet still carnal.
Now, as Christians, we are free from sin, but do we not sin nevertheless? We even make some very big mistakes. Tell me, my brethren, have any of you lied since you converted? Have any of you sworn? Blasphemed? Lusted? Lashed out in anger? Christians, though free from sin, still continue to sin. It's just a thing humans do. In the same way, though Christians ought not be divided, it's just human nature that we continue to be so.
In some ways, this can make a denomination useful. One purpose of the Church is edification and education. We pool our knowledge as Christians. You may not have read the Bible from cover to cover. I might have read it from cover to cover less times than my pastor. Perhaps I understand one specific area really well, yet another Christian just can't grasp it on their own. So we gather together, we pool our knowledge, we teach each other. Denominations, at least when they form as a result of this, can be helpful. It becomes a problem when the thoughts and traditions of denominations are treated as if they are equal to, and even greater than Scripture.
So you see that denominations are really just one more frailty of human society. It's possible to be a Christian and claim one, and I don't even think it's necessarily sin, but at the end of the day, denominations are a division in the Church that we really ought to seal up. We can rely on them to teach us what we do not yet know, but there is a great deal of difference between "Scripture says" and "my denomination believes". At some point, we're all going to have to get off the milk that is our denominational statement of faith, and get onto the meat that is the written word of God.