Now returning to gelilah: Rabbi Yehoshua Neuwirth (Shemirat Shabbat K’hilchato vol. I, 15:52) notes that one may tie the belt even if it will remain tied for an extended period (albeit not a full week of seven days) since it is for the purpose of a mitzvah (securing a Torah scroll properly).
Nowadays it is common to use either an elasticized belt with a buckle or a belt with two Velcro fasteners; thus the entire question of tying and untying the belt on Shabbat is rendered moot.
In the same vein, some people prefer wearing loafers on Shabbat to avoid the problems of tying and untying shoelaces. It seems that your son has chosen to do this for now. As regards a necktie, there really is no halacha that states that one must wear one, so if that’s his choice, so be it. It is possible that he will resume wearing lace-up shoes and a tie at some point, and since his current practice has a basis in halacha it may be best not to pressure him one way or the other.
May continued discussion of hilchot Shabbat and scrupulous observance of the laws bring us to merit a yom shekulo Shabbat with the advent of Mashiach speedily in our days.
Rabbi Yaakov Klass, rav of Congregation K’hal Bnei Matisyahu in Flatbush, Brooklyn,is Torah Editor of The Jewish Press. He can be contacted at firstname.lastname@example.org.