Yeah, it's normal to read other people's role plays. I've been doing it ever since I joined Gaia. It's how I learned to rp.
RPs are just stories that people write together, and some of them are good entertainment to read.
I'm not butting in in any way, or posting without permission, so I don't know why anyone would have a problem with it.
That's why we have the Library thread, so people can go read over interesting rps and maybe even be inspired to make similar ones.
If you really want to keep everything private, my suggestion would be to RP over Private Messages, or using Skype, Discord, or other chat programs where you can set it so only you and your rp partner can read it.