If a toilet gets clogged on shabbos can one use a plunger to fix the toilet on shabbos in case of need?
It is permitted to use the plunger, but one should preferable use a non-Jew or one’s weaker hand.
The Shulchan Aruch writes (Orach Chaim 336:9) that if a drainage gutter is blocked with grass and straw, causing a leak in one’s home, it is permitted to clear it with one’s feet, by means of a shinui. The reason for this is that in case of a great loss, the Sages did not enact the prohibition involved.
The Mishnah Berurah explains writes that one can clear the blockage so that it won’t interfere with the water flow, but it is forbidden to totally remove the blockage. This involves a prohibition of boneh, building.
Concerning a toilet, some rule that it is permitted to use a plunger, because it is very easy to clear the toilet (see Minchas Yitzchak 5:75). For a toilet, there is special reason to be lenient, because it involves an issue of kavod ha-brios. However, the Minchas Yitzchak writes that one should preferably use a non-Jew, or his weaker hand.
The Be’er Moshe is also lenient, explaining that the case is different from the case of the gutter, in that one needs only to push some of the blockage through (like pushing cocoa through a blocked straw). This is also stated by Binyan Shabbos, ps. 18, 303, in the name of Rav Shlomo Zalman Auerbach.
However, Rav Moshe Feinstein (Iggros Moshe 4:73) writes that one may only unclog a toilet with a plunger if it is partially stuffed, and water can still flow through (it is then permitted to use the plunger if it can be cleared with one or two pushes). He adds that if a toilet is regularly clogged, it is permitted to clear it, because this is not considered fixing. However if the toilet is totally stuffed, and this does not occur regularly, then it is considered a maaseh uman (expert labor) to clear it, and is forbidden on account of uvda de-chol. If there is a great need and an issue of kevod ha-briyos, one can clear the toilet by means of a non-Jew.
Because clearing the toilet is a pressing issue and involved kevos ha-beriyos, one can rely on the lenient opinions.