First, as being the means of bringing persons of obscure birth into undue distinction, and raising men to honours which their fathers and grandfathers never dreamt of; . . .. A man is in greater danger in the navy of being insulted by the rise of one whose father, his father might have disdained to speak to. . . than in any other line.
But then we get blindsided by the decree that Muggleborns have obviously stolen magic.
Now, I have no doubt that a totalitarian society could do such thing. As Theodore Dalrymple observed,
In my study of communist societies, I came to the conclusion that the purpose of communist propaganda was not to persuade or convince, not to inform, but to humiliate; and therefore, the less it corresponded to reality the better. When people are forced to remain silent when they are being told the most obvious lies, or even worse when they are forced to repeat the lies themselves, they lose once and for all their sense of probity. To assent to obvious lies is...in some small way to become evil oneself. One's standing to resist anything is thus eroded, and even destroyed. A society of emasculated liars is easy to control
On the other hand, it would lead to a lot more conflict and discomfort with the ridiculousness of it. Like the prisoner who was poisoned and killed while trying to escape.
But then I was pondering what sort of rhetoric would be likely. Slughorn, we know, does not really believe in his bones that a Muggleborn wizard can be as powerful as a pureblood. There's also the possible of how these Muggleborns just don't know how to act -- parvenus, you know, have no taste, and really are a corrupting influence on purebloods. Worsre, they are more likely to violate the statutes of secrecy -- which, in fact, come to think of it, is probably true, having spent the first decades of their lives not learning strict habits of secrecy. Or that Muggleborn wizardry is wild and uncontrollable. Or they have no discretion in using it -- which is also conceivable, Muggles, not raised to know what it could and could not do would probably try to do things out of fairy tales or mimicking technology, which could be extremely dangerous.
But none of those would lead to accusations of stealing magic. Indeed, in all of them, the theft charge would probably raise suspicions of paranoia. OTOH, we don't actually hear any theory of Muggleborn wizardry. A curious gap in the curiosity. It would have a lot of interesting implications starting with the obvious that you would want to de-magic Dark wizards. But there it is.