The only issues we've ever seen are where someone is alergic to some of the substances, some people do have dairy, or tomato, or both, skin allergies. Whenever that's come up we've just stopped using those substances with those people, in the same way we wouldn't use dairy-based substances with vegan models.
Not ever had anyone complain of acne-type issues though. One thing we are big on is very, very thorough clean-up, with the girls hosing each other down with gallons of water, and very thorough hair-washes with lashings of shampoo and more gallons of water. Make sure people are taking a really good, long shower, ten or twenty minutes with the water flowing at maximum, not just a quick in and out.
I remember I had this issue one of the first times I ever got pied. I found that oil and dairy based messes tended to cause that reaction when left on the skin for prolonged periods of time.
As with any mess, it's best to use a facial cleanser until you notice that slimy feeling on the skin goes away. Be sure to exfoliate and cleanse the pores as well. Lastly, a good moisturizer really helps smooth the skin after using all those cleansers.
Wam ingredients (on the face) do not 'cause' acne,rather, if you are prone to acne 'breakouts', then certain substances (esp. anything oily) on the face will irritate the skin and promote breakouts (due in part to clogged pores)...chocolate is another trigger. One thing to do to control the inflammation that initiates a breakout is to take an NSAID (like ibuprofen; one or two pills at 200mg each will do) before wamming (where your face gets covered). And yes, if you're allergic to dairy, that's a problem...best to substitute cream for Cool Whip, or, the (dare I say it) shaving cream. Then wash your face thoroughly with warm water and mild soap afterwards.
Nothing singlehandedly causes acne but if you use certain oils or thick products that would have heavy polymer chains then this could certainly unbalance the skin and cause a breakout of spots as it clogs the pores
In theory, anything fatty or oily might exacerbate acne. However, the amount of time the stuff is actually on your skin will be short for most people, so it shouldn't be a big issue. Certainly less of an issue than for example working in a kitchen with a lot of fatty food cooking would be.
Just make sure you don't leave it on for too long, and wash thoroughly using something that breaks down fats (anything soapy would be fine, or some kind of more gentle cleanser if you're concerned about dry skin) and you should be fine. If you want to be totally sure maybe stick to non-fatty substances like methylcellulose or similar gunge.