This doesn't answer your question, but consider that acne vulgaris is mostly a product of a modern, high glycemic diet & lifestyle - discussed in this previous /askscience thread, and that chimps don't have the same access to this kind of diet.

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What about the macaques in Bali that steal ice cream from children and bags of food from people shopping in town?

Haha OP I would like to know where you were when the idea for this post came into your head and why please?!! 🤣

I lived in the tropics for a decade and had pet monkeys. I realised they aren’t chimps but they never had spots and they ate just about everything

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Isn’t the majority of issues nowadays as a result of the excess sugars and lack of exercise people expose themselves to..

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This is pure speculation, so take what I say with a grain of salt. I always saw acne as a result of our loss of hair in some places. Oil might keep hair healthy in chimps, but if there is no hair, it just collects on the skin, combines with dirt, and clogs pores.