If they don't take Amex, I use a VISA or MasterCard or a Discover card. Really no big deal at all.
I can't imagine not patronizing a perfectly good establishment that I would otherwise choose to, just because they don't accept 2 of the ~8-10 cards in my wallet. OTOH, if they won't take ANY credit card, and only accept cash, I very well might pass on them unless they were somehow exceptional relative to other choices.