None of those things characterise theories of multiple racisms, and none of them was what Abbott was saying. Noting that racisms are different is not putting them in a hierarchy. The experience of being black in the UK is different to the experience of being black in France, even. It’s not that one racism is somehow better in one country than the other. But they need to be understood differently — historically, culturally, politically, sociologically — in order to be addressed in their own context.
I don’t think it was dismissive of other types of racism at all. It was just saying that experiencing one type of racist phenomenon doesn’t make you an expert in a different racist phenomenon. Being at the receiving end of anti-semitism is different to being at the receiving end of anti-black racism. The social processes you employ to address one will not address the other. The problematisation of race/ethnicity/culture/religion is different in each case, and so the solution you need is different.