Is it permissible to open a gym in the West where both genders can mix freely with an intention to create an environment for exercise? If it results in sin, isn't it true that any gender mixing can cause it such as at restaurants?
Any work or act or business which causes or leads or results in sinful act is not permissible. Making both genders mix with out proper Hijab is not allowed in Islam. Usually gyms in western countries don't care for proper Hijab, that it why Muslim should not indulge himself in such business which can lead to sinful acts, otherwise he will be responsible and his income from such sinful business will not be lawful.
Wassalam.