1. Copyright Infringement: If the religious music used by the dance studio is protected by copyright, then performing a routine to that music without permission could constitute copyright infringement. This would be especially true if the dance studio is charging admission or otherwise profiting from the performance. In such cases, the copyright owner could sue the dance studio for damages or seek an injunction to prevent them from performing the routine again.
2. Freedom of Religion: The use of religious symbols, such as a cross, in a dance performance could potentially raise issues of freedom of religion. In the United States, the First Amendment to the Constitution protects the free exercise of religion. This includes the right to perform religious rituals and express religious beliefs. However, this right is not absolute and can be limited in certain circumstances, such as when it interferes with the rights of others or threatens public safety. In the case of a private dance studio, it is possible that some people could argue that the use of religious music and symbols in a dance performance is offensive or violates their religious beliefs. However, it is also possible that the dance studio could argue that their performance is protected by freedom of expression and that they have the right to use religious symbols and music in their artistic work.
Ultimately, whether a private dance studio could be sued for performing a routine to religious music and having a cross as a prop would depend on the specific facts and circumstances of the case, as well as the applicable laws and regulations. It is important to note that this is a complex legal issue and it is always advisable to consult with an attorney for specific legal advice.