What does It is useless for the sheep to pass resolutions in favor of vegetarianism while the wolf remains of a different opinion by William Inge mean?

The phrase is saying that people without power passing resolutions is pointless when those with power will simply ignore those resolutions.

A similar one is mice voting to bell the cat. (ie putting a bell on a cat so they will hear it approaching.)

It is no use the mice voting for this if the cat will not allow it. They can do nothing about it, they have no power over the cat.