One of the biggest issues when it comes to respecting other occupations is the lack of exposure to what they do. Most people know what their job is, and how busy they are, but never consider other people to be as hard working, or as important. You see less of it in the navy, because you live, eat, and work alongside everybody else, but on a base the average person don't really interact with people outside their unit often, or for long periods of time.
Even in Afghanistan, I never really interacted with RCD, PPCLI, or RCR guys on the same FOB as me. We all did our own things, and sat at our own tables when the cooks were serving fresh rations. On ship I interacted with all of the departments pretty much every day, even alongside.