Work with your history. You do have a history, right? If not, go and write one now, then come back to this answer.
While it is true that many holidays are religious - in fact the word derives from "Holy Day" - holidays are also inspired by other events such as military victories or defeats (such as ANZAC Day or Remembrance day), or by important milestones in public history, such as gaining the right to an 8-hour working day as opposed to a former 12-hour working day, or by sporting events (such as Melbourne Cup Day or AFL Grand Final Day) that people ignore work to attend anyway.
Most of your holidays will be annual events on a given date, but some that date back to events that occurred before the modern calendar was developed (for whatever value of 'modern' your world's calendar has) may be associated with particular seasons and/or astronomical events such as the phases of the moon(s), and may or may not occur every year, and thus may not occur on a single date.
For example, a certain important religious event may have happened as the first snow fell in the Holy City one year, and the holiday that is associated with this event may occur each year with the first snowfall of the year - either on the Holy City (in which case, people celebrate when they hear that snow has fallen there), or in their own location (what happens when there is no snow in that location - ever?). Our Christmas is traditionally a winter festival, so there is a certain amount of dissonance when celebrated in the hemisphere opposite to that in which it was conceived - Consider the incongruity of singing carols about snow in furnace-like summer heat.
In these sorts of cases, it is important to know not only when a holiday was conceived, but where, and to where has it spread since its conception. I've heard stories about a Japanese department store wanting to celebrate Easter one year, and because of the inexperience of the (primarily Shinto) staff in charge of setting up the Easter display with Christian traditions, the store set up a display of a crucified Easter bunny, which remained in place until it was pointed out to them that this was in fact inappropriate. However, your world may not have had someone to correct a holiday's misconceptions, and a holiday in this particular place and those settled from it may have what other people consider quite outrageous features as a consequence.