If you're considering cloth toilet "paper" I strongly recommend experimenting with different fabric types first rather than assuming any old thing will work, or even that carefully chosen soft fabric will work.
Stretchy knit fabrics stretch instead of wipe.
Thin fabrics bleed through so stuff gets all over your hands.
Plush fabrics are only soft if run through a dryer - line drying transforms velour into harder stuff that absorbs well but has a bit of a sandpaper effect.
Smooth woven fabric is ineffective.
All of these could be used if there was really no other option, but if you're planning on washing for re-use it makes sense to me to have items worthy of the effort, especially for SHTF. I recommend cotton flannel.
With enough rags you can use and throw away, but I consider the time and effort of cutting them into suitable pieces is too dear a price for one time use.
One way to reduce the amount of resources, effort, and time put into washing is to use a single rag multiple times for urine only, letting it dry out in-between uses. To each their own, of course. If in a well ventilated area and placed on a heater or in the sun there really isn't any smell, and it's dry by the next time you need it. It sounds grosser than it really is.
On the matter feminine hygiene, it's important to note that there are many menstrual cups other than the Diva cup that vary significantly by size and material. What fits one woman doesn't necessarily fit the next. What's comfortable for one woman doesn't necessarily work for the next. Most cups are silicone, one is natural latex, one is a kind of plastic. The silicone cups range from very stiff to very soft, and everywhere in-between. Some come in different colors. Some have caused allergic reactions (though a very rare occurrence). My point is, just like all other preps if you go this route you want to do your homework and try it out first to make sure it's a viable alternative. Guys, this one really is strictly the woman's department. This site
is by far the best resource I've found for comparing cups, answering FAQs, and generalized non-biased information about anything and everything related to cups you ever wanted to know (and perhaps some you didn't). Cups don't break*, scratch, or wear out, and they're small enough that having one or two around really isn't much of a burden as far as storage space is concerned.
I personally think that after TEOTWAWKI menstrual cups would be in extremely high demand as a barter item. The convenience of a tampon coupled with the fact that it's infinitely reusable and sanitary (even with little or no water) and requires very little time or effort to wash would make it the winner, hands down.
*One company had an issue with cups splitting and now sells them as a sample promotional item, on guaranteeing single use. Also, I'm not sure the rubber cup has the same durability as the silicone ones.
Another option not yet mentioned is natural sponge tampons: http://www.jadeandpearl.com/catalog/index.php
They are reusable for a few cycles. Personally, I haven't tried them and I don't plan to. I have read of someone who just purchases regular natural sponges and then cuts them to size, which seems much more economical than the overpriced "Sea Pearls".
An alternative to pads that's both more comfortable and results in less fabric to wash is small pieces of folded fabric that are applied and hold in place on their own (but not like a tampon). In order to work well the fabric should be a very loose knit and as thin as possible; other kinds of fabric barely work, do not hold in place and can be quite uncomfortable. I stumbled upon this fabric
(Natural Light Lattice) as the best by far. A ballpark size is 2" X 3", smaller for light days. You can get away with soiling much less fabric because the only material used is where it's needed. Since the fabric doesn't ravel, making them is as easy as a pair of scissors. I discovered this method out of necessity but have found it a superior option to pads.