No interpersonal conflicts--I call shenanigans! As long as people live together, they will have interpersonal conflicts simply by virtue of their proximity to one another. Some people will have differing ideas regarding how to solve a problem, some people will come into a conflict over a "scarce" commodity (we both want the promotion, but only one of us can have it), and some people will just have personality conflicts.
No Religion--no matter whether you are religious or not, it's hard to imagine that religious beliefs that have existed since humanity began (whether monotheistic, polytheistic, or other) that somehow, humanity will shed all religious belief in the next 200 - 300 years merely because we advance technologically. (This really only applies to TOS and TNG where religious people were relegated to "primitive" cultures)