Oh, let me make myself clear. You'd only steal someone's soul if you deliberately tried to. If two people trusted each other, they could hold hands without much fear of getting their soul sucked out. Babies probably wouldn't be able to steal their parents' souls (I've decided), they wouldn't know how to use their ability.
Most likely, children would be repetitively told from a young age not to touch anyone, and to not let strangers get too close to them. People would most likely wear full-body clothing and get nervous if other people went near them. Romantic relationships would take far longer to get to intimate stages. There'd probably be a myth of a shadowman who sneaks up on people and steals their souls, and there most likely would be thieves who would harvest people's souls.
What really needs defining is how the souls could be used to perform magic. It wouldn't be very useful to steal people's souls if all it did was work like Breaths in Warbreaker. In fact, it wouldn't even be that effective if it taught you everything the person who used to own the soul knew. Now, if souls granted magical power that couldn't be used up, each soul increased this power, and the power was something ridiculously powerful like being able to throw large fire-balls or mind-control people or... anyway, that really needs defining. Another question is, if gaining someone else's soul gave you those powers, would each person's own soul give them these powers?