Hello, Henry. Yes, I feel relaxed when interacting with non-believers. That's unless the non-believers are determined to ridicule religion and Christianity in particular. If that is the case, conversation becomes difficult.
Fortunately, most people with whom I would talk about personal matters and values have better manners than that, so it isn't a big problem anyway.
At the same time, there are also belligerent believers, so it's not just a problem with non-believers. Catholics, particularly recent converts, are often in that category, imagining (or having been taught) that their church is the special target of criticism from other Christians.
After all is said and done, I think that the best way to handle "world people," both the critics and those who are just not believers, isn't to debate with them but to quietly show by your own lifestyle how your faith manifests itself. Kindness, charity, respect for others, and etc. can go a long way towards changing the attitude of non-believers.