I use a "wet sanding" method for just about everything - including MM - that keeps the abrasives from clogging, and as fas as I know is perfectly safe for every type of wood and synthetic (and cured finish):
I hold a paper towel dampened with Mineral Spirits in my left hand, and the MM or sandpaper in my right.
The sandpaper goes UNDER the work, the paper towel on the top, and I move them in unison back and forth along the work with the lathe turning. Anything that is released by the sandpaper is picked up by the paper towel, dust is reduced ten-fold, and the abraisive never clogs.
MS will not raise the grain and will not harm the adhesive on the abraisive. As an added bonus, my sandpaper lasts longer this way, too.
When using the method on oily wood, it also has the advantage of cleaning off any oil on the piece which helps your finish adhere better.