Is it better to wear wool tzitzis? indicates that it is better Halachically to wear a woolen Beged with woolen Tzitzis. Recently I met a fellow who the entire week wears cotton Tzitzis, yet on Shabbos wears woolen Tzitzis. He indicated that this is mentioned by Poskim (did not remember which ones), yet I have been unable to find a source. Is there a source to wear woolen Tzitzis on Shabbos, more than during the week?
Yeshuas Yaakov Orach Chaim 9 mentions that due to the fact that a Beged made from other materials it is not clear if it is obligated in Tzitzis Biblically or Rabbinically, if it is not obligated Biblically then how can you go out into a public domain with them on Shabbos?