I can't understand the problem, really. If you both have the confidence to be in each other's phones, then there's nothing wrong in checking the history. My OH checks my mails and I check his for practical reasons, and as we share really everything, neither of us considers going to the history as a trust issue. But I guess that depends on the relationship you have.
Regarding porn, I guess most people watches it. When I was younger I felt it was degrading but now I realise there are lots of different types of porn. I don't mind at all to watch a Marc Dorcel movie, for example, whereas national productions are too cringy for me. Maybe you don't like now and never will, but it's not immoral for him to watch it, and it doesn't mean that he doesn't like you or anything, it's just natural. Sex is everywhere - movies, series, telly, etc. - mostly very light or erotic only, but even in popular music there's lots of references and pretty much everyone has sex - like Bill Hicks said, "Guess what? We're here - someone's been f*****g". And so, this thought of porn as something out of the devil's work ends up being pretty hypocritical, even though I don't think that all of us must like it - I think we just shouldn't be as judgemental of that. There are way worse things in the world that nobody cares about with as much passion as they do speeches against porn.
As someone said earlier, he probably looked up the animal stuff as a joke, or out of curiosity. It doesn't mean he is into it. I know most people are saying that you should just leave it, but in your place I would talk to him, say that I looked up his browsing history and what I found, and then ask him what he likes or doesn't like. Not in a condemning way, just as a normal topic. But that will depend on your trust level. If he doesn't trust you, he will probably be upset you looked up the history. But if you are going to be worried, I would just be honest and talk to him. But it's up to you.
(I would probably just be very worried if he was looking up child porn - now that's a red light.)