Some woods do indeed react differently to different approaches to finishing. It may be best to test out various methods of preparing your blanks before turning and finishing ...
Oily woods can be dried out enough on their surface that penetrating finishes that don't usually do well on oily woods could still be applied (soak wood in 90% rubbing alcohol or acetone) ...
Cocobolo is a wood that happens to have oils in it ... during the final stages of dry sanding, I clean my blank with 90% isopropyl alcohol, though acetone would probably work a little better, as it has no water in it. Once I've sanded it to 1000 grit, I clean it again with alcohol and then immediately apply Minwax (natural wood color) stain and seal, followed by the first of several coats of superglue. I haven't had any issues with this method so far... no haze, no cracks. After I have a sufficiently thick layer of CA on the blank, I wet-sand with micromesh pads up to 12,000 grit and follow with Plast-X to polish, and a coat of Turtle Wax Hard Shell as the final coat.
I haven't found any woods yet that this approach has not worked for, but I'm still fairly new at this game.