You can absolutely pet the penguins. Just, don't. As far as king and emperor penguins go, anyway, the adult ones have no land predators so they're pretty much completely unfussed about people approaching them.

Another thing, though. People see an African penguin or an Adelie or similar at a zoo and they think all penguins are little cuddly football sized waddlers. I imagine most people would be completely unprepared for the sheer scale of an adult emperor penguin:

And if you mess with the penguins, you're messing with me.