How do you remove dried shave cream from ceramic tile and grout?

If the polish is a petroleum based product it will probably require a solvent type cleaner to modify the chemical structure of the polish. Start by removing as much as possible with soap and water. Then graduate to Mineral spirits on up to acetones or toulene products. May take several tries and re-saturation. Might also try commercial products such as "Goof Off" and or steam!

Water based is easier! Soap & Water to start and commerially available products with a sodium percarbonate ingredient[an Oxidizer], if the stain is presistent. I use a brand called Oxiclean that works well.

I recommend any grout be sealed with with a waterbased Low VOC penetrating sealer that soaks into the grout where it reacts with alkali found in all Portland Cement products. This forms a solid inside to waterproof any cement material. I have beige tile with white grout in several high traffic areas, including a kitchen! Six years old and looks brand new! After the StableCrete application, I poured Grape Juice in an area to test it. After the liquid evaporated a soap & water sponge removed the grape stain residue. Walla -- White grout joints!!