I don't know why she was attracted to Dodi Fayed. It does seem like scraping the bottom of the barrel. I wonder if she used Fayed to not only make Khan jealous, but to get people "used" to the idea that she was with a Muslim. I don't know how to explain it but Fayed was unsuitable in so many ways that she may have hoped people would accept Khan as a step up and not focused on his religion.
I think it was more a case of thumbing her nose at Charles and the RF; she knew very well what they thought of the Fayeds.