I mean, technically you're both. All half-blood characters in HP are wizards/witches anyway, and most of them in general would be too. I think either a) the racist elements in HP world saw them as tiers of "depravity" with one overiding the other (although, I don't know which order they'd go in) or B) people with the sense not to openly oppose muggle-borns still jumped on halfbloods because they could get away with it, so you only ever heard one or the other.
You're also a scientifically created being in a magical world, so you may create yet another form of discrimination, or oddballs like Mr. Weasley may ogle you uncomfortably. uwu