Conclusion: The wrong assembly grease can have serious consequences, especially with silicone and EPDM.
No animal or vegetable fats or oils may be used with EPDM. This is because EPDM swells extremely with this type of medium and soaks up like a sponge.
With silicone, care must be taken not to use silicone grease. (like with like is not compatible)
Otherwise, the assembly grease can be freely selected for all other materials listed.