I don't think IABU to object to this - but how bad would you say it is?
Yesterday when I went upstairs to put DS to bed I left my laptop on, with email and MN open. While I was upstairs DP went through my email and read everything in my sent items folder, which he would have had to click on to get to, so not like it was just left on the screen.
There was nothing incriminating in there (!) as I've got nothing to hide but I felt it was a bit invasive and sneaky of him to go through my stuff when I wasn't there. I wouldn't have minded if he was looking for something, like a recipe or a photo, but he was just reading them for no reason (or to check up on me most likely). Likewise I don't hide my emails from him, but he doesn't know the password and tbh this is the reason why. If you trust someone why would you need to spy on them?