There is nothing wrong with the GOP, or the Democrats, being able to get the e-mails of public officials and public workers.
I see no reason why the Democratic Party shouldn't do the same thing. Every bit of knowledge you have about a candidate is a bonus.
Sure, it's natural to just send an e-mail to a co-worker and think nothing of it. The last part is the issue. You may no longer "think nothing of it." Not in today's environment.
I have made it a practice to never discuss any sort of contentious internal matter on my company's internal e-mail or chat system. If I want to discuss how I think management is doing with one of my co-workers I do it in private e-mail and on personal phones/texts. On work e-mail, I stick to "Just the facts Ma'am."
If you are on any sort of e-mail/text/chat/team sites with co-workers I advise you to never, never use them for personal reasons. Never use them for union organizing. Never use them to air your complaints about management. Private enterprises OWN all of that communication and are free to search it at will. Governmental systems are, as you can see, far more open to search by unintended people. People who will twist every word you type, and take it all out of context. Do not give either private employers or the public that opportunity.