well......despite the fact that both mouthpiece of a pipe and some saxophone mouthpieces are both made or ebonite, there is a difference which is removing any material from the tip, rails and the chamber of a mouthpiece will alter the mouthpiece performance.
So, if the best advise is don’t let your mouthpiece ever get to that point, but if you need cleaning it that much ...you probably should do that only with the parts that are not involved with sound production.
This kit seems to be working well (although I imagine it takes a little more than a good rub with both components).
Component 1, says the ad, is sanitizing the mouthpiece but clearly has to contain some agent apt to dissolve some of the offending dirt and removes scratches by means of abrasion
I've no idea to be honest Milandro. I saw the link over the other side and thought it would be worth posting here so the 'pros' and 'cons' can be looked at in some more detail. It was mentioned that some vintage 'pipe stems' can be expensive, so I guess owners wouldn't want to be rubbing to hard.
As long as one stays on the top and sides with the cleaning, it should be ok. I looked it up and Caranauba wax is ok to ingest. Dr. Omar Henderson of Dr's Products has a Ph.D. in research chemistry. I communicated with him one time about restoring old ebonite mouthpieces that have begun to break down and give off sulphur. He said the process would be too dangerous to trust to a layman, but he would do a chemical restoration of mouthpiece for about $50. Obviously this is more involved than cleaning the outside with an abrasive and giving it a coat of wax.