Any kind of petroleum-based grease will contain emulsifiers, surfactants, and especially breakdown products, that could attack petroleum-based plastics and rubbers. This property will increase with age, as the petroleum breakdown is accelerated by exposure to heat and UV.
In short, the use of petroleum-based lubricants can accelerate the "natural" heat and UV degradation of certain plastics.
For vinyl, plastic and rubber...particularly on interior parts...I would advise you to stick to silicone-based lubricants (or perhaps synthetics that specifically state they are OK for use on plastics--though this is a distant second best, in that these products will still contain emulsifiers and surfactants that can soften or damage certain plastics).
2004 Buick Lesabre Limited, Gran Touring; Bone Stock
1998 Buick Lesabre Limited, Gran Touring; Mods: Poly sway bushings/endlinks, Tru-Cool trans cooler, Thrasher shift kit (med), PLIM, front PEM; Mods in progress: Alot of stuff, but slowly...