Thanks! I think it's quite reasonable to reject choice and take as an axiom that all sets are measurable, so I'm interested in the consequences of it. I'd always been told that the continuum hypothesis is orthogonal to everything people care about, but that's only after assuming choice.
CH is orthogonal to ZF. CH is orthogonal to ZFC.
If ZFC is inconsistent, then ZF is also inconsistent.
AC is orthogonal to CH.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.