First, I have to point out that that chart is overly simplistic. There are at least eight distinct systems I know about, between ancient and modern, Jewish and Christian. There is no unified "Protestant" version; in fact, Lutherans use a numbering and division more similar to the Catholic one than to other Protestants. As to your question about dissent within the "Protestant church," the answer is clearly yes, and doubly so because there was never a single unified Protestant church.

The Western tradition that the Catholics and Lutherans mostly share goes back, as does much of their theology, to Augustine, Bishop of Hippo in the late 300s/early 400s. The twist that this chart calls "Protestant" (and is indeed used by many Protestants of different traditions) comes, to the best of my knowledge, from John Calvin, in his Institutes of the Christian Religion, where he cites concern for clearly proclaiming the prohibition against idolatry and graven images as the reason:

There is no room for controversy as to the fact, that the Law is divided into ten heads since this is repeatedly sanctioned by divine authority. The question, therefore, is not as to the number of the parts, but the method of dividing them. Those who adopt a division which gives three commandments to the First Table, and throws the remaining seven into the Second Table, expunge the commandment concerning images from the list, or at least conceal it under the first, though there cannot be a doubt that it was distinctly set down by the Lord as a separate commandment; whereas the tenth, which prohibits the coveting of what belongs to our neighbour, they absurdly break down into two.

Institutes, chapter 8, section 12. Now, Calvin studies is not my strength, and the Institutes went through a large number of editions from 1536 through 1559, so I'm afraid I can't speak confidently as to when that dates within that range. Already in his 1545 Geneva Catechism, Calvin has changed the numbering away from the traditional Catholic/Lutheran system, so I feel comfortable thinking it may be from an earlier edition of Institutes. It's worth noting that the Eastern Orthodox divide them in a way that, like the majority Protestant method, makes graven images its own commandment, but I'm afraid I don't know about the connections there, if any.

That's just the earliest and clearest example I know about for the reordering, but it wasn't the first example of iconoclasm motivated by the commandment against graven images during the Reformation; in 1522, Andreas Karlstadt led a bout of it, and was rebuked by Luther, who specifically treated that command as a sub-section of the first commandment, "You shall have no other gods before me."