The polymers used in modern sabots has and probably still is an ever growing process of change. The new sabots we use are not the sabots of old. The polymers used in their production have undergone an upgrading if you will, to make them even more rifle friendly. I have shot thousands of sabots through modern muzzleloaders. No harm to the rifle has been done. That's not to detract from the importance of a good solvent and brushing from time to time, just to make sure that no build up of anything is happening. But this solvent and brush cleaning is also aimed at copper, lead, and other impurities building in the barrel. As well as sabot residue, should it ever occur.
There is no cleaning between shots needed reference the sabot itself. When shooters clean between shots it is normally more aimed at powder fouling. As we know, when fired, a muzzleloader burn creates in many cases a fouling that can lead to further loading problems, or decrease in the accuracy of follow up shots, if this fouling is not at least minimized. The cleaning between shots insure that the degree of powder fouling remains somewhat constant. But it is not to remove any plastic that might have been left behind from the sabot.