Actually, you have this backwards. Remember that soap batter
will actually clean
your stickblender when you go to rinse it off. Nothing caustic will remain on it, because the NaOH will either be saponified with the oils, or it will quickly convert into harmless soda ash due to contact with the air.
In contrast, a greasy lotion will be harder to wash off the stickblender than any soap batter will be. But honestly, either one rinses off pretty easily if you soak the blade and shaft briefly in hot water with Dawn, then reattach it to the stickblender and give it a good whirl in that hot soapy water.
What you really need to consider is the potential contamination of your products, not your food. For instance, lotion is far more likely than soap to go bad if any food particles remain on the stickblender.
In contrast, soap batter has the benefit of the high pH and the caustic nature of the lye, which kills anything in any small food particles that would otherwise cause spoilage of the finished soap. People put all kinds of food products in their CP soap batter, and have no problems with that as long as it's not chunks of unblended food.
For these reasons, I tend to use one SB for lotions, gels, etc., and a different one for soap, and a different one for food. But for years, I used the same SB, crockpot, spatulas, etc., for soap and for food. No one in my house has ever died or even be sickened by this. It's pretty easy to clean everything sufficiently with hot water, a good grease-cutting dish soap, and a little elbow grease.