Can one fold one’s talis after davening at shul and replace it in the talis bag, or would this be considered preparing for the next Shabbos? If I cannot fold it, I would fear that it might really wrinkled by stuffing it into the talis bag, and so on.
It is permitted to fold the tallis after davening, but one should fold the tallis not according to its original creases.
Sources: Shulchan Aruch (Orach Chaim 302:2) writes that one may not fold a tallis after davening on Shabbos (unless very specific conditions are met — see there), a ruling based on the Mishnah and Gemara (Shabbos 113a), yet concludes by quoting an opinion stating that folding a tallis not according to the original creases is permitted in all cases, “and his words seem to be correct.”
Mishna Berurah (Orach Chaim 302:3-18) explains how we rule in this matter, stating: “Because this type of folding has no lasting effect and therefore there is no liability for transgressing [the labor of] metaken (lit. fixing) [on Shabbat] at all, it is permitted in this manner even in the event that one of the four above mentioned conditions [i.e., folded by one person only, new garments never laundered, white garments, and where no other garment is available to change into] is not met, and even if there is no intention to wear the garment [again] on that day [Shabbos].”
Yet, after explaining that this is how latter authorities have ruled (which is the meaning behind the Shulchan Aruch’s acceptance of the leniency), he adds that “he who wishes to be more stringent and not fold at all, that is [considered] far better.” Following this, Mishnah Berurah concludes with the statement of Magen Avraham regarding the making of beds on Shabbos. Although the making of beds is generally prohibited as the preparation of something needed later, after Shabbos, it is permitted to make the bed if (the bed is in a room that one frequents and) it is unpleasant to leave the bed unmade, as making the bed has thus become a legitimate need of Shabbos itself.
This would apply to a shul, too, which would become very untidy if everybody left their unfolded tallis lying around. Yet, following the ruling of Shulchan Aruch, one should fold the tallis not according to its creases. There is no need, however, to make remarks to those who fold their tallis along original creases, for eretz hachaim writes that this was the ancient custom (in Halab). As regards the problem of metaken, Aruch Hashulchan (Orach Chaim 302:11-12) essentially agrees that there is no violation of the melachah when one folds in the way that we do, which is not derech uman (the way of a craftsman). [See there for a discussion of the possible prohibition of tirchah, unnecessary exertion on Shabbos.]
“Stuffing” tallis into a bag (or somewhere else) is not a solution. In the words of Aruch Hashulchan, leaving the tais entirely unfolded is not “the way of human beings!”