I don't think I have ever had a friend who wouldn't have some secrets. The only thing that matters is if something indicates that their secret poses some threat to me. If I had a suspicion they do some criminal activity or have an affair that could ruin a few people's lives, I'd be out. I also wouldn't want to be around someone who constantly censors oneself, severely limits topics we can talk about and paranoidly self-checks if they didn't say something they didn't want to reveal.