My only concern is a mineral-oil based grease which could adversely affect the plastic part (not knowing what type of plastic that particular part is made of). So a synthetic grease is preferred. Plus, since plumbing grease is used on devices where contamination with ingestible components, such a grease must be pretty inert, therefore adding to my recommendation for use on plastic. Additionally, it's cheap and readily available.
But as Phil said I might just use what I have on hand. SuperLube would be my go-to, though it has a teflon component in a mineral oil base.