Is shift cable protector under bottom bracket on cyclocross bike important? I recently replaced the shifter cables on my cyclocross bike (Specialized Tricross). Both cables run exposed (not in cable housing) under the bottom bracket, through a little screwed-on plastic guide that keeps them in place. 

When I removed the old cables, one of them also included a short, maybe 8-10" piece of what I would call protective plastic sheeth that kind of sat within the screwed-on plastic guide, extending for a few inches out either side. It was pretty shredded up and I decided to chuck it. 

Now that I'm looking at the new cables (approx 200km riding), I'm wondering if I should have looked for a replacement for that protective sheath. 

Is that protective sheath important and should I have replaced it? If so, what is it called?

The image below shows the cables right now, looking straight up at the BB, front of bike towards top of image. 

I saw this similar question, but it seems like the OP there did not at any point have the protective sheath I originally had on my bike.
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.