Growing up, my mother always asked me, "who are you talking to?", "what are you thinking?", "what book are you reading?", and on and on.
Therefore, as an adult, I don't like it when I'm texting or calling someone, and someone asks me about it. I don't have anything to hide. It just seems intrusive to me. However, this is my experience.
If you feel someone is being unfaithful, it would be better simply to talk about that, rather than to keep asking who they're talking to or texting. And no, I don't believe that snooping on their phone is justified. If you feel that they won't be telling you the truth when you ask about it, you might want to re-think the relationship.