The question of whether you have to add preservatives or not depends on what your microbial testing tells you. In general, there is a low probability of growth in an anhydrous product. That is why some companies don’t add it. The stability from a microbial standpoint could be years.
However, there isn’t a no-probability of growth. Consumers can get moisture on a product and microbes could grow at the interface. Or your product could get contaminated during production.
For these reasons it makes sense to add a preservative even to anhydrous formulas. And the other thing to consider from a scientific standpoint, is that there are zero negative effects of including a preservative “just in case.”
The only reason for avoiding preservatives is to support a fear marketing campaign. Unfortunately, many consumers buy into this fear so I understand why companies do it.