I totally agree that if something seems dodgy and you need evidence, it can sometimes be necessary to look on your DP's phone to confirm your suspicions (this was how I proved exH was cheating - I screenshotted some conversations after I'd accidentally found paperwork showing he'd booked a hotel with her!)
However, I think going through their phone, especially without their knowledge, implies a lack of trust and an invasion of privacy and is not a good place for a relationship to be in.
Despite being cheated on in previous relationships, I wouldn't dream of looking on current DP's phone unless he was showing me something in particular. We both leave our phones around unlocked and if I found he was looking on my phone to see who I followed on social networks / was talking to (without VERY good reason) I'd be gutted.
Thoughts?