I remember watching the whole Jade Goody debacle end to end (BB to her death) and the first time I learned she was mixed race was right now. There was absolutely no general consciousness that she was anything but a working class (or rather underclass) white woman at the time. It certainly never came up even when she was being accused of racism during the whole Shilpa Shetty mess. I think the pig thing was more bout her being overweight, blunt of feature and obviously lower class, and crass etc. The class angle was huge, tbqh.
I do remember Graham Norton, after joining in on the pig meme and Jade-bashing for weeks, suddenly reigning it in and asking everyone to be nicer, rather hypocritically. I think there was a realization that the hate train had gone way too far and there was a concerted effort to rebrand her, not to mention a realisation that someone with THAT much fame (or notoriety, whatever) would be good for making a few people in the media and beyond some money well after the fact.
Speaking of which, did any other BB stars get their own perfume? Jade Goody had two (Shh and Controversial), and you can still buy them, weirdly enough.