On many Outward Bound courses, toilet paper was left at home and local natural items substituted to cut down on backcountry environmental impact. In some desert environs, where the most popular substitutes of snow or vegetation weren’t available, toilet paper was carried and then burned or carried out. It should be obvious (but unfortunately not to all) that burning toilet paper is a great hazard in forest fire conditions, so carrying it out was then prefered.
In some damper times and places, burning works well. Here is what I like to bring (in addition to using snow and other substitutes). Weighs 23 grams and is enough for 2 weeks.
Tiny cuben fiber stuffsack lined with thin plastic for water tightness.
14 half sheets of paper towel (more durable than tp and burns readily)
7 feet of jute cord
I cut a 6″ section of the jute cord and fuzz it up and use it to catch a spark from a mish metal flint which then catches the paper towel and with care will burn the whole thing to ash.