Is it permissible to display handmade crafts for sale in an exhibition that is not free of mixing (of genders) and music, given that the exhibitor will not be present?

It is not forbidden to display works in an exhibition that contains reprehensible things, for it is like other markets, many of which are not free of reprehensible things. It is incumbent upon the Muslim to offer advice to the best of his ability, and there is no blame upon him if the reprehensible thing remains. Allah Almighty says: (So remind, for you are only a reminder; You are not over them a controller) and He says: (O you who have believed, upon you is [the responsibility for] yourselves. Those who have gone astray will not harm you when you have been guided). So, whoever fulfills the obligation within his capacity has been guided.