Based purely off of your Q: there's no problem whatsoever as long as he washes his hands. This is actually a very common into to tasting solids for kids 6-12 months when they're first being introduced.
Yes, using utensils (spoons, chopsticks, whatever... I was only allowed to use chopsticks with my nanny) teaches fine motor control... but you're not really concerned with fine motor control when you're first introducing foods/ tasting. Also... babies don't eat easily... but they DO spit things out easily. The only way to keep something they don't want in their mouths is to hold it and their lips shut. Even things they WANT in their mouths tends to ooze out while they're learning the oral fine motor. So if she doesn't want it, she's not going to be swallowing it.
Based off of what others have said: this looks like a co-parenting argument? That you're looking for ammunition?
The finger won't be it. However, you can adjust your parenting plan so that no foods other than breastmilk (or milk & formula) be allowed for x # of months. Unfortunately (or fortunately depending on how you look at things), however, both parties have to agree. My best friend's mum fought for years for over the diet her kids ate at dad's house, but because dad was giving them a healthy diet (just not what her mum WANTED them to eat, and when, and how, and how much) she never won in the courts. She was basically told that her time was her time, and dad's time was dad's time... and that neither were allowed to dictate what happened on the other person's time. The only way she was legally allowed to dictate what happened was if dad agreed in writing, or if she sued and won full custody.