Would creating an application for sports club, nutrition clinic, and physical therapy offers—knowing that music and mixing are present in most of them—cause us to incur sin if people use it and go to these places?

There is no objection to creating an application that guides people to permissible things, such as shops, clinics, and clubs whose activities are permissible. There is no sin upon the developer of the application if these places play music or involve gender mixing, as long as the original and predominant activity is permissible. The sin falls upon the one who directly commits the forbidden act. However, if a club is frequently characterized by widespread immorality and corruption, then it is forbidden to guide people to it, based on the Almighty's saying: (And cooperate in righteousness and piety, but do not cooperate in sin and aggression. And fear Allah; indeed, Allah is severe in penalty). And whoever calls to misguidance bears the sin of those who follow him.