Read the System Administrators' Code of Ethics and take it to heart. Even if your job title doesn't include the words "system" or "administrator."
It's actually pretty easy to ignore the content of an email if you're focused on the email delivery process (mail server logs, the headers of forged/spam mails, things like that). Similarly, if you're doing FTP hosting or file drops for customers, you rarely need to dig into the content of the files themselves to troubleshoot upload/download problems. There are rarely reasons to dig into the content of whatever you're working on. It does come up, if (for instance) some piece of email has wacky malformed content that keep crashing the mail client, but IME those situations are uncommon.
I used to work at a mom-and-pop ISP, in a small town. Our customers included the local police and fire departments, City Hall, and most of the larger law offices and accountants' offices. Since we provided email and Web hosting (among other services), I certainly could have made some locals' lives very interesting. Hell, I had access to the email of everyone in my company, including that of the owners to whom I reported. I'll admit to having been tempted once or twice, but I'm proud to say I never abused my privilege.