Yes, people here are absolutely fine with that. You probably come from a very different world culture-wise. First of all, second jobs are not the norm here. It's rather rare, actually and most second jobs are hobbies you take money for, like photography or the like. Your employer will almost certainly not even bother to ask any further.

Secondly: your employer cannot object just because they don't like your face. There are set criteria. They will object if your second job would conflict directly with your first job, that'd be if you work at a competitor, would have work hours in your second job that conflict with those of your first job or would work too much all together. That's it.