There are certainly places where you should burn or pack out your toilet paper, but unless the privy instructions state otherwise, the moldering privy isn't among them.  In fact, the toilet paper acts as an additional bulking agent in the composting process.  Just keep the following aspects in mind:

1. Follow the instructions at the privy if there are any.
2. Don't use large quantities of toilet paper.  For environmental purposes, you should practice some frugality in the use of toilet paper anyway, but especially in the case of the moldering privy.  It increases the volume of material in the crib, decreasing the time before maintenance will be required, and increasing the time to completion of the composting process.
3. Use 'bio-degradable' toilet paper where available.  While toilet paper generally is all 'bio-degradable' the paper that is tagged as such disintegrates more quickly.
4. Definitely do not use toilet paper with perfumes and dyes, which can be toxic in the environment, and can impede the decomposition process.  Toilet paper rated as 'bio-degradable' will not have perfumes and dyes.

If you want to pack out your toilet paper, go for it.  Just keep it where I can't see it.