I'd prefer he didn't look at my phone, not because I have things to hide, but just because he is my boyfriend doesn't give him rights to the personal conversations I have with my other friends because often they are confiding in me.
But if he asked, I'd probably say yes because we are really open with each other.
And if I asked to look at his phone, not that I would, I think I'd be suspicious if he said no just because like I said we are open with each other. But yeah, I guess what I said about me and having personal convos with friends also applies to him so I'd understand hopefully.