To properly address this question one must deal with two distinct issues. The first is simply what to do when there is no prepared toilet paper for Shabbat. The other involves dealing with the concern of possibly insulting friends who have different halachic standards on certain issues.
The overwhelming majority (at least) opinion is that one may not rip toilet paper from a roll on Shabbat. One who rips it on the perforation, which creates a measured piece of paper, violates the melacha[1] of mechatech (cutting). If one rips off a piece in an unmeasured manner (e.g., not on the perforation), it is a matter of considerable discussion whether he violates the Torah prohibition of korei’a (ripping for a constructive purpose) or just a rabbinic violation of metaken kli (fashioning a utensil).[2] The crux of the issue is whether korei’a applies to a case where one cuts a part of an object from the rest of the object in order to use only one of the two parts.[3]
Several poskim rule that where there is no viable alternative, one may rip the toilet paper in a way that only a rabbinic law, not a Torah one, would be violated.[4] This is based on the principle that in cases of significant need of k’vod haberiyot (preserving human dignity), rabbinic laws may be pushed off.[5] Although we need to apply this rule with care,[6] we do have precedent for using something muktzeh as toilet paper.[7] One can make the issue a rabbinic violation by tearing the toilet paper in a significantly unusual way. (Using elbows and legs are among the poskim’s suggestions, as is wetting the paper away from the perforation so that it will rip easily in a halachically less severe manner.)
This, of course, assumes that there is no other way to deal with the k’vod haberiyot issue without ripping the toilet paper. Other solutions may be available. The most direct solution, if the problem is discovered in time, is to ask the hosts for tissues or pre-cut toilet paper (one may open a package by destroying it), which they may have forgotten to put out. One need not be ashamed to ask – it probably has happened to all of us. On the contrary, one who says nothing can cause embarrassment if the hosts discover later that they put their guest in an uncomfortable situation. A more difficult question arises in situations where one is convinced that the hosts are unaware or have purposely been lenient (with an unusual rabbinic ruling or without one) on the matter.
What would happen if one would raise the need for pre-cut paper, either explicitly or with a statement like “I didn’t find the Shabbat toilet paper”? This may not be pleasant for the guest or the host. However, the alternative could be that the hosts will find out years and many guests later that they were unaware of or not careful about something that their peers were and they had put their guests in uncomfortable positions. If the hosts will not listen or you are in a community where you are one of the few who is careful on the matter, then one can, in many cases, apply the rule of mutav sheyihiyu shogegin (it is better that people violate something unknowingly, or partially so, than knowingly).[8] It is trickier when a person might listen, but he is in a fragile religious state where he could also react negatively to what he sees as religious meddling. We cannot address the guidelines in a paragraph, as a book would be needed. The basic advice is to be smart (including bringing your own provisions to a home where you expect such a problem).