If Lily's parents are squibs then Harry cannot trace his geneology unbroken through many generations of wizards. Being a descendant of squibs as well as a muggle lover is reason enough for V & Co to dislike Harry (especially throwing in there the profecy, the involvement in the Order, etc).
With regards to the term 'mudblood' I think that it is used in a derogetory manner towards anyone no matter what the parentage but typically used towards muggle-born wizards. In a way this could be similar to our use of the word 'bastard' (though much more mildly!). Technically it means of person of unmarried parents but is used derogetorily, usually in anger or frustration, to any person. Obviously this is a much milder analogy, but you get the idea (and I didn't want to run the risk of offending anyone. . . )!
I think it all boils down to the fact that we don't know much about Harry's grandparent (both Evans and Potter) or what's up with Petunia (the fact Dumbledore referred to her by her first name as he does with his former students. . . .)
Sarah
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