In 610 there is no Quran, no Islam, no Muslims. Muhammad dictates the Quran later in his life, and by 640 there is the Quran in the form we know it today, and Islam, and Muslims, all at once. It emerged very discretely and with relative unity.

For Christianity, there is a historical record of Christians as early as Nero's reign, but the earliest books in what is now the New Testament don't get written until the end of the 1st century AD, and as far as we can tell are not written by anyone who witnessed the life of Jesus on Earth. And then the canon isn't formalized until almost 3 centuries after the Crucifixion; meanwhile, there have been lots of parallel and related religious movements going on that get sorted out by councils of elders/bishops long after the fact. The Old Testament/Tanakh was written by dozens or even hundreds of authors, over a period of at least 700 years.

There might be historical and cultural revisionism going on, as you'd see anywhere, but Islam emerges clearly in a moment, as opposed to Christianity which is the product of much longer and more blurry processes. This makes for much less ambiguity over what Islam does or does not look like.

My experience of Islam largely comes from roommates who had the Quran very thoroughly taught in schools. I got the impression that there's a lot less picking and choosing; it's a package deal that you either wholly embrace or don't.