What are the issues in oiling or polishing the drone bores?

These issues always cause heated arguments, but are inherently related in that they both address roughness on the surface of the bore.

A rough bore acts like a filter to remove some of the harmonics of the sound. In general, smoother bores have more high frequency content in their harmonics. Polishing or oiling results in a smoother bore and increases the fraction of high frequencies coming out of the drone. Depending upon your point of view, this may or may not be a good thing!

A rough bore also presents more surface area for absorption of moisture from your breath into the wood. Oiling for minimizing moisture uptake is discussed here.  Rough surfaces have more surface area and, therefore, take up moisture faster and potentially result in a more rapid build-up of stress. If the rate of moisture uptake is slowed sufficiently to allow equilibration of the moisture level between the wood on the inside and outside of the drone, the wood will not build up stress and will not crack. Once the wood is equilibrated to a humidified level and the drone is played regularly, the moisture level in the wood will not change and the drone will not split.

The roughness of the bore can be treated by either oiling or polishing. Oil or wax creates a water-resistant layer that slows the uptake of water into the wood, it also fills in the imperfections in the wood surface making the surface smoother. Polishing reduces the surface area available for absorption of moisture and thus keeps the rate low. Both techniques will reduce moisture uptake. Both approaches will alter the sound of the drones.

The advantage of commercial bore oil is that it is temporary. If you are treating an old set of pipes, a complete coating or layer of mineral oil over the entire bore surface will form a water-resistant layer which provides a reduced rate of moisture uptake to allow the drone to equilibrate its internal moisture content over several weeks so that the risk of moisture related stress cracking is reduced. The tone will be affected during this time period because the smaller imperfections in the surface will be filled in. However, if you stop oiling the drone after this critical period, the residual mineral oil will loose its its effect on bore smoothness after several weeks and the tone of the drone is unaffected. It's really the best of all worlds.

Polishing can be done commercially, or can be done at home.  Be sure you want to permanently alter the tone of your drones.  There is no way back. Many hobbyists suggest using #0000 steel wool on a rifle cleaning kit or equivalent. My current preference is to use wool yarn wrapped around a spring steel rod.  (Yes, it's slow, but it's also coarse enough to do the job, while being soft enough to do no damage if you slip.) (Note: If you remove enough material to increase the diameter of the drone, you will raise its pitch and you'll have to compensate by sliding the drone top up higher on the peg. Even if you don't remove any significant amount of material, the "effective" diameter of the smoother bore will be increased over the original and your tuning will be affected requiring a higher drone position. )

If your bores are already very highly polished, there is probably very little surface area for moisture to absorb through and very little surface roughness to remove upper harmonics, so oiling or polishing would not have much effect. On the other hand, a rough, dry bore may be ripe for splitting, and oiling may cause a significant tonal change.

My advice would be that mineral oil won't hurt in the long run. I'd avoid any other treatment until you form an opinion regarding the sound of your pipes. If you like what you've heard with mineral oil, you can make it more permanent by waxing (which seems to last about a year) or you can mechanically polish your drones bores.

It would be irresponsible to not relay that there are anecdotal stories that oiling caused old drones to crack. However, I don't see any reason why oil should cause drones to crack and suspect that 1) insufficient oil coverage/penetration was provided followed by 2) uptake of moisture and 3) stress build-up inside the wood. Drones which are already cracked, but not humidified will reveal their cracks upon humidification. Humidification of the drone from a very dry state results in some expansion of the wood. Oiling cannot prevent an existing crack from opening up.

Other references include:

an excellent, independent description of the interaction of wood, oil and water

a study of cracking in oboes and clarinets using Thompson's Water seal