Mishnah Berurah — משנה ברורה

Is forbidden - See in Magen Avraham where he concludes that this that the Rem"a is stringent [regarding] during the week, is not referring to what he wrote at the beginning "Even [regarding] a טלית קטן...", because [regarding] a טלית קטן, if it became known to him that the ציצית were invalid, which would be a big embarrassment for him to remove it from under his clothing, whether he's in the synagogue or in public, he is not required to remove them, for [we say] that where there is a big embarrassment, human dignity overrides even a Torah level prohibition which has [an element of] "sit and don't do"(ie. he is passively transgressing). But he [still] needs to hurry home or to the room before the synagogue and remove it there, even if he's involved in a mitzvah in the synagogue, since it's a Torah level prohibition. But on Shabbos, he does not need to hurry out of the synagogue as long as he's still busy with the mitzvah. And if one sees that his friend's ציצית are severed, he shouldn't tell him until he gets home, meaning, he should call him over to his house and then tell him to remove it. the Magen Avraham wrote further that if there are no ציצית in the city, the law during the week is the same as on Shabbos. And the same applies regarding a טלית that requires ציצית only on a Rabbinic level, for example: a borrowed טלית after 30 days [have passed], it's law is the same during the week as on Shabbos.