That is for each individual couple to decide. There's no singular answer to this.

As individuals, we all have different needs for privacy. Some people have higher needs, some people have lower needs. My wife doesn't understand why I close the bathroom door to pee... I don't understand why she thinks it's odd that I do.

When it comes to access to each other's email, it's important that each partner is allowed to establish their own boundaries, and to talk to each other about those boundaries. Some people make the assumption that if you don't want your spouse looking at your email, you must be doing something you shouldn't.... personally, that line of reasoning doesn't fly with me. This isn't a place where you can demand one partner conforms to the other... saying "I'll let you look at mine" doesn't give you a right to demand to look at theirs. Some people just have different boundaries on their life / privacy.

Some of us just like to close the door.