Ashkenazim also hold it is forbidden to put your fingers through your tzitzis on shabbos for the melacha of unknotting on shabbos which is one of the 39 melachos.
What you might not know is the middle lane…. Some people just on shabbos when they put on their tallis and make the Bracha they just put their fingers between EACH SET OF STRINGS versus during the week when a person’s fingers go into the middle of each corner set in order to get the strings untied. Thus when you are just going by the group between each corners set of strings on shabbos they may in fact still be knotted up on the middle of the 8 strings since a person’s fingers only went between the 4 corners stick of strings