How important is it to use natural peanut butter?

I always use natural PB when the recipe calls for it. Natural is usually just peanuts, oil, maybe salt. The processed (i.e., Skippy, Jif) includes a boatload of sugar so watch out if the recipe adds it, that it isn't too sweet. Also, the consistency of natural PB is much more... "drippy" if you will, than regular PB. I think you could use regular PB, just watch the sweetener, and you may have to add a little water/oil to thin it out.

It depends what you want to use instead. Store bought, commercial peanut butter (like Jiff or Skippy's) contains other ingredients, besides peanuts, which can impact the flavor or outcome of the Pavlova. Natural PB should be just ground up peanuts