Today's post starts with a story from the first time I lived in Japan. At the time I was going to the Kyoto Center for Japanese Studies, which was located behind the zoo. We had a joke about how it was an appropriate place for gaijin...
It was a wonderful school, and while I went there, I did two different homestays. The first one was what I would call sub-optimal - but how was I to know? I soldiered on for quite a long while, believing that my dissatisfaction must be caused by cultural intolerance, until I realized there were really some substantive issues there (like not being given a heater and waking up to find the temperature at 3 degrees C in my room) and switched homestays.
This is not so much about them, as about how I felt about a month in. I got depressed, and I couldn't figure out what I was missing until one day I walked into school and saw one of my friends and said,
"Please give me a hug!"
I can't tell you how much better I felt after that. I'd gone for about a month with nobody touching me at all. It made me terribly lonely.
Touching is one of those things that varies widely across cultures. I remember seeing a show once about an African group of people who engaged in constant social touching, and finding this to be very interesting (but not particularly appealing). On the other hand, I love giving hugs to my friends, and I missed it very deeply for my first few weeks in Japan (before I knew my classmates too well).
In high school I remember there were marked and unmarked forms of touching. Shoulder massage was considered flirtatious but didn't "mean" anything; hugs were safe with just about anyone; holding hands was something you never did except with that someone special.
This is a place where you can really create nuance and social meaning for the purposes of your world. It's not a binary "we touch" or "we don't touch" kind of thing. It can be "this kind of touch is safe," "this kind of touch is awful," "this kind of touch is sweet" - or embarrassing, or not to be done on penalty of death, etc. My only suggestion would be not to make it random. There are always reasons for the consequences of different kinds of touch: social messages like those of male-female bonding, or taboos associated with parts of the body or particular types of activities (for example, a certain type of touch might only be permitted when in mourning etc.).
As you create your society, think through the rules of touch, and you'll find you can send many more messages about your world than you could without them.