Aunt - I guess you could reconcile them by emphasising the 'some degree' and possibly downgrading 'solidarity' to 'common cause'. After all, history is littered with examples of political movements aiming communally for one particular thing, despite their members disagreeing on plenty of others - hence the way revolutions etc often subsequently break down into infighting.
So long as feminism is seen essentially as a large interest group - i.e., something which all (/many) women are pursuing because it benefits each of them individually (though possibly to varying degrees) - then this is not really problematic.
I think where the inconsistency creeps in is when feminism takes on a moral aspect, which it actually does in most people's arguments - even liberal feminists rarely see their motivation as pure self-interest. At this point it becomes problematic because the ethical arguments for feminism are largely based in doctrines of rights, and the same arguments that support women's rights also tend to support the extension of rights to other underprivileged groups. So, in this view, there is a logical inconsistency in being a feminist but not worrying about other inequalities.
Which I am guessing is what Felas means here:
"the ethics of talking about my own oppression while simultaneously taking advantage of my privilege over someone else… makes me feel very uncomfortable."
I think the position that support for one underprivileged group logically entails support for others is correct. (I am also pro a more radical and less capitalist version of feminism because I am not convinced that the issues of invisible and emotional labour can be resolved within the capitalist system, and other reasons, but this is wandering from the point).
However, practically, I worry that the 'support for one disadvantaged group entails support for all' line of thought leads to an absurd situation in which you are not allowed to try to make any efforts to change the social system unless you are addressing every conceivable inequality with in it, which paralyses any change at all (essentially the move that the 'women shouldn't hire cleaners' argument in the OP is trying to make). On the other hand, still thinking practically, the risk of pursuing liberal feminist objectives without addressing other inequalities - so hiring the cleaner etc - is that it alienates poorer, or otherwise disadvantaged, women who (probably correctly) perceive themselves to be benefiting only marginally from feminist advances, while those advances give major benefits to women who are exploiting them in other ways. (See that extremely instructive thread a while back about women of colour and their attitudes to feminism).
That's my take on it anyway.