[PJ]

Doesn't matter who you're talking to on the other side. Girls, guys, family, that's not the point.

When you're texting someone, that conversation is between you and the other person. If there's something you want to show or talk about with your SO, or anyone for that matter, that should be under your discretion only. Your SO shouldn't be able to barge in and look at whatever he/she wants, and whenever he/she wants.

It makes sense to have a password, so you let your SO look at your phone under your supervision only. That way they're not snooping when you're sleeping, in the shower, etc.

Different relationships will have different boundaries. But relationships with zero boundaries are not healthy.
Some people are more open, others are less.