Indeed, although only if it's an issue that would affect everyone equally. As I say, it's hard at this moment to see a situation whereby it would be a massive issue in the UK now.
But say a country with a slight Muslim majority over Christian used an initiative to ban alcohol and pork (God, why...
The California thing is called "initiatives". The main argument against it is that when you take the representatives out of the equation, you can end up with 'Tyranny of the Majority' - where in a population where perhaps 60% are A's and 40% B's (A and B can be what you like - ethnic groups...