I don't find the term "Mudblood" offensive. It's rather more of a complement. Confused? I'll explain.
So, the story of Adam and Eve.
Adam was made of clay, and clay is technically mud. He was jut a normal human.
Wizards were made by "Lady Magic."
So technically, muggleborns blood IS made of mud, since their anscestor was created from clay.
And it's more of a complement because even though they were just a normal human, Lady Magic found them worthy enough to be blessed with magic.
And I'm not Christian (my friend is, and that's how I know about Adam and Eve), but Purebloods probably heard the story from muggles, and when the first Muggleborns came, they called them "mudbloods" as a complement, because they were seen as worthy by their creator.
And the term slowly became an insult and an offensive word over the decades, and the original meaning of the name was lost.
