There was a lengthy debate on this somewhere - it could be the "Animal rights" thread or the "Do you eat meat?" thread. Don't remember.
Anyways, I think that animal liberation is very important (obviously); domination over other sentient beings and exploiting them for our own use to the extent we do now is objectionable. I'm not going to be ridiculous and say that everyone should become vegan (I know that won't work), but we can all agree that the level of meat production now is just wasteful and environmentally harmful, as well as degrading to the lives of the animals.
But I don't know if I'd say animal liberation is inseparable from human liberation. Saying they're inseparable suggests that the liberation is joined and liberation for one party will mean liberation for the other.
I do not agree with groups like the ALF/Earth First etc that put animals before humans though, and I believe as Communists that we should not take that stance either. It leads down to the slippery slope of primitivism and deep ecology that plagues the radical environmental movement.