PFPE oil-based products have potential to be the most effctive, longest lasting, and most gentle on rubber, from what I've gathered - but also the most expensive. An example of a product in this category is DuPont Krytox oil or grease. Some auto manufacturers (VW, BMW) also have weather seal maintenance products in this category.
Petroleum or hydrocarbon-based oils should be avoided on rubber to prevent damage. An example of a product in this category is Vasoline.
Silicone oil products are sort of in the middle-of-the-road in terms of how good they work, how long they last, and to what degree they may damage the health of the rubber. Although they are far healthier than hydrocarbon based oils on rubber, supposedly, they can dissolve waxes out of the rubber, (which are there to prevent oxidation and "dry-rot"). An example of a popular product in this category is called Gummi-pfledge.