Derech Hamelech: Isn’t hesech hada’as a much more pertinent issue?
BoR: While technically you do not have to wear tzitzis every moment of the day, please bear the following in mind. An Israeli soldier once asked Rav Shlomo Aviner if he was permitted to take his tzitzis off during physical training (which includes full kit marches in the desert in the summer). The Rabbi answered “technically yes, but remember that Bar Kochba’s fighters fought in tefillin.”