The best cleaning product ever invented is the baby wipe. Everyone should have a stash of baby wipes handy. Of course I didn't know this until I had a baby, and my wife is the one who brought this tip to my attention. They are inexpensive and easy to use. You can get them at any department store, grocery store, or drug store and they come in boxes of hundreds or small packages that fit in a purse or glove compartment.
Baby wipes are safe enough to put on a baby's skin but strong enough to clean up all kinds of messes. In our home we have used baby wipes to get marker out of couch cushions, makeup out of carpets, and who knows what out of clothes. We always make sure we have baby wipes in our home and in our vehicles.
I don't know if there is anything that a baby wipe will damage. I'm sure there is something but we haven't found anything yet. We use Huggies brand and Kirkland Signature (Costco) brand but I'm sure any brand will work the same.