Is shift cable protector under bottom bracket on cyclocross bike important?
The thinking with them is to protect the contact point from contamination and provide a slick surface, reducing friction. They do achieve that to an extent, especially early in their life. 

The problem is when the liner itself starts junking up with grime that can't be easily removed, it will then cause friction problems itself. For this reason, I think going without is fine in many cases.

Some bikes use them to prevent cables from rubbing the frame on painted surfaces, raw carbon, etc. In that case I would not recommend going without.

You can get replacement pieces from inside shift housing. Take a long piece, cut the outer plastic down it longitudinally with a razor, then whip it hard against a hard surface. The wire strands will come apart and you can take the liner out.