Conscious means "having an awareness of one's inner and outer worlds; mentally perceptive, awake, mindful."

So "conscious business" might mean, engaging in an occupation, work, or trade in a mindful, awake fashion. This implies, of course, that many people do not do so. In my experience, that is often the case. So I would definitely be in favor of conscious business; or conscious anything, for that matter.

Be Silly. Be honest. Be kind.