It doesn't seem to be intended for the standard ones
This only relies on the line:
Challenge Rating: As a normal skeleton + 1.
Which suggests that getting the two variants wouldn't increase the CR by +2, just by +1
But it is intended to be possible for the Classic Horrors Revisited ones:
(...) the following variations can be stacked with one another—it’s possible to have an exploding acid skeleton, for example
My guess is that designers of Classic Horrors Revisited were not on the same page than the one writing the bestiary, so maybe your GM will want to patch some things here and there (an obvious one being to make the CR increase with each template).
The multiplying rule states:
When you are asked to apply more than one multiplier to a roll, the multipliers are not multiplied by one another. Instead, you combine them into a single multiplier, with each extra multiple adding 1 less than its value to the first multiple. For example, if you are asked to apply a ×2 multiplier twice, the result would be ×3, not ×4.
The number of HD is not a roll, so there is no reason to apply the x2x2=x3 rule: a skeleton with two variants would count as four times its HD when raising it.
As a sidenote, about stacking different skeleton templates
It is impossible to have, let's say, a "bloody skeleton burning skeleton goblin" (with twice the skeleton template with different variants)
The skeleton template has a prerequisite (emphasis mine):
“Skeleton” is an acquired template that can be added to any corporeal creature (other than an undead) that has a skeletal system (referred to hereafter as the base creature).
And among other effects does:
Type: The creature’s type changes to undead. (...)