Generally Talis Gadol is wrapped only for prayer, not as a simple jacket. If someone has to wash his talis gadol, but the only place he can wash and dry it in his apartment is in the bathroom, can one take a tallis gadol into a bathroom or the like to be washed?
The Piskei Teshuvos 21:footnote 50 addresses this and writes that it is permissible to wash a talis in a restroom even if it has a toilet since the achronim held that there is no ruach raah in such a place.
text of Piskei Tesuvos:
In addition, Rav Ahron Mordechai Green (Yalkut Halichos Tzitzis 22) also concludes that it would be permitted.
Text of Yalkut Halichos Tzitzis 22: