Question: I was recently invited to a friend’s home on Shabbos and saw them folding serviettes at the table into different designs. Is this permissible?
Answer: The Shulchan Aruch (OC 302:3) writes that one should not fold regular clothes on Shabbos. While different reasons are offered for this prohibition, Rambam (Shabbos 22:22) writes that folding is being mesaken, fixing the garment (See Aruch Hashulchan OC 302:12).
Thus, R’ Yehoshua Neuwirth (Shemiras Shabbos Kehilchasa 16:19) quoting R’ Shlomo Zalman Auerbach, writes that one can’t fold paper into hats and boats or create origami shapes on Shabbos.
Nonetheless, he writes (ibid. 11:40) that there is no prohibition of tikkun mana, finishing products, with disposable paper products. Thus, one may fold a serviette into a simple shape. Making fancier shapes is prohibited, though, as it is comparable to boneh, assembling something.
R’ Ephraim Greenblatt (Rivevos Efraim 1:223:8), however, writes that R’ Moshe Feinstein allowed one to fold serviettes, arguing that the reasons to forbid folding clothes don’t apply to disposable serviettes. Likewise, R’ Moshe Stern (Be’er Moshe 8:134) writes that there is no issue of boneh with such serviettes, and one can fold them into any shape.
In conclusion, while it is preferable to fold them before Shabbos, one can fold disposable serviettes even on Shabbos if necessary.