I always keep skincare with me, and ask them to wash their face or remove any residue myself prior to application. For brides i will usually do a little "mini facial" with cleanser, toner, moisturizer.
They seem to really appreciate and enjoy it, and it makes things easier on me. I'd rather have the peace of mind of knowing that I'm starting with a clean slate (ALOT of people dont properly remove makeup, particularly eye makeup), and that theyre using a moisturizer that will work well with the makeup, and not one that may have hidden SPF, etc. Its absolutely not rude at all.
My skincare kit usually includes all of the following, though some i purchase in travel sizes or split into smaller bottles to save space:
Almay Eye Makeup Remover Pads
Ponds Exfoliating Makeup Wipes
I use these two first, prior to any cleansing. Almay pads are GREAT and get rid of seriously stubborn eye makeup, and the Ponds wipes are a great gentle exfoliator.
DHC Cleansing Oil
Cetaphil Cleanser
Cetaphil for most, DHC for dry skin or skin that has alot of makeup residue i need to cut through. I'm hoping to pick up some Dermalogica precleanse soon as well, I've heard a lot about it.
Dermalogica Toner
Paula's Choice SPF free moisturizers (one each for very dry, normal, and oily skins)
Rosebud Salve (for lips)
Aquaphor Ointment
I love paulas choice.. cheap, fragrance free, spf free, doesnt fight with the makeup, does what it says it will.
For my emergency kit for tricky skin problems, i use:
Kate Somerville ExfoliKate (serious, but gentle exfoliation, super fast)
Skyn Eye Gels (for dehydrated, dry, angry looking undereyes)
I would rather pack a skin care kit than run the risk of having my makeup application ruined by bad skincare... great makeup starts with great skin, so i think its worth it. And lets face it.. a lot of people are not very nice to their skin. At my trials for brides i try to offer some basic recommendations for skincare to make sure they're looking their best the day of.. however, i am also an esthetician so I'm not sure the legality of someone who isnt licensed for such things making these types of recs.
Regardless though, it makes a huge difference and you shouldnt be afraid to carry a skincare kit and make sure you're starting with a clean slate.