Never had this when mine was a baby as baby groups were held in local halls etc. We were all mums with messy LOs so all knew the consequences of being within reaching distance of grabby hands.
When I took DD out I would make sure I'd keep her as clean as poss (and this was in the days just before wipes so a damp flannel was always in my kit), to avoid her messing up both myself and others. I never had this happen to me, but would have apologised and offered to pay without being asked, whether the other person was being a bit precious or not. My child, my responsibility.
DD had a similar experience to you a few weeks back. Despite my nagging warnings, eyes were off the ball for a few seconds! These things happen. She apologised and offered to pay for dry cleaning immediately. Diffused potential embarrassing melt-down immediately (DD reckoned she was almost certainly a child-free, professional type - bit like DD pre-baby).
Funnily enough, we'd had the "what would you do" when we were out in a restaurant last summer (past 9pm), where the parents of a toddler were in a group and just letting her wander around the restaurant with a chocolate bar (I think I remember mentioning a chocolate bomb was about to go off!), and I was wearing white trousers.
Well, chocolate bomb DID go off on another woman's cream dress. Toddler's family hadn't even noticed she'd gone halfway across the restaurant until Mrs Cream Dress shot up, knocked both chair and toddler over and screams ensued. (Toddler unhurt, but startled.)
Toddler's family were almost feral in reaction - frightening to see the aggression flare so quickly - blaming Mrs Cream Dress. Half the restaurant had seen this coming as toddler had bothered most of the patrons at some point during the evening. Owner had to come over and break it up. Then he had to offer a free meal to Mrs Cream Dress as compensation towards the cleaning. Toddler's group were asked to leave.
I don't think it was up to the owner to compensate, but it was pretty obvious nothing was forthcoming from the toddler's group. It went through my mind for days after that someone could have snatched that little girl and her family wouldn't realise until it was too late - but I digress. This (hopefully) isn't a common situation and has nothing to do with OP's question as such.
I still believe that when you're out and about with LOs, you need to be responsible for their actions and have a bit of thought for other people. They may be on their way to an important meeting or a variety of other situations that they don't envision coming across LOs with sticky fingers. They may also have no experience of children and don't expect or realise how fast they can move when they want to.
The woman in question may have been a regular at the coffee shop but not have come across your group before. I'm assuming it was busy at that time, and a bit cramped. She may have had a stressful morning and needed her cuppa. She probably has no experience with children. She was just a perfect stranger expecting to relax. I don't think YABU with regards to the way she reacted as such, but I do think YABVU the way you did.
Your child, your responsibility, you pay. Keep it calm and civil, and never over-react, even if other person is acting like a total witch. Walk a mile in their shoes before you judge.