Yes photos are allowed, at least they were when I was there less than a decade ago. There is a whole bunch of politics over who runs things with the church specifically, because so many different denominations are involved, and when I was last there they even had to compromise and have the Armenians (there is a whole quarter in the old city for them) deal with opening and closing the doors. There are a lot of weird rules about who is allowed to do what that pertain to the church leadership and how its run, but people can just enter the church. Israelis have attacked people outside of the church, but that's not like a law, that's just Jews being assholes to Christians.