To be fair, things like day, month, and year can all have very definite non-arbitrary time periods. And some of the other stuff, like missing the ritual because of day-light savings time is the kind of thing I wouldn't expect to show up in a story unless it's a comedy.
But I do get your point, and I'd love to pull something like this on a group. Have a full moon only happen every 6 months or conversely have it happen every 6 days, or have prophecies demarcated in other counting systems.