I haven't read the book so maybe the context would change my interpretation. But from your excerpt, I'd take the phrase to mean that people in general were, to use the definition you quote, relaxed and not easily worried about safety. The society was generally safe, so people didn't obsess over it.
One could imagine a society where people don't care about safety. They accept danger as a part of life, and when someone does something dangerous, it's just "oh well, life is dangerous".
One could imagine a society where people are obsessed about safety. There are long books of rules about how to keep safe. People are scrupulous about what they eat to make sure it won't harm them. They worry about the possibility of dangerous chemicals being in any product they use. Etc. (Sort of like 21st century America, I'd say.)
And one could imagine a society in the middle. A society that is generally safe, and where people are so relaxed in this safety that they just don't worry about it. Or where they accept small dangers as unavoidable, that some dangers are so small that protecting yourself from them is not worth the effort. I'd call that a society with "easy-going safety".