I think the only safe thing to do would be to use plastic bags (or sheets) as a barrier. I know I had some MPC era sets that only had thin tissue paper between the cars and the styrofoam. The tissue got thrown out immediately, so the cars got put "naked" into their respective slots in the foam case. For years those sets sat in storage (other than during Christmas season) with no adverse effects. Hard to tell what styrofoam is made out of these days, so you may want to use a barrier to play it safe. I know exactly what you are talking about, as some plastics "gas off" i.e. that net looking rubbery stuff people use to line shelving. That stuff is nasty and highly reactive against certain plastics and vinyl. I have purchased used equipment packed directly into the foam packaging that were fine, I'd just hate to recommend that and something bad happen!
Stack