THIS IS THE.....UNITED STATES OF AMERICA AND YOU CANNOT FIRE SOMEONE BECAUSE OF THEIR RELIGIOUS BELIEFS.
True. No one can be terminated because of their religious beliefs.
People can be terminated because of their conduct even when that conduct occurs as a result of their religious beliefs though, but the circumstances where you can do this in the U.S. are extremely limited.
The employer must be able to show that the objectionable duty is a primary and indispensible part of the job, that the job cannot be performed apart from this duty, and that it is not something that can readily be performed by other employees.
In other words, although the employer is willing, even desirous of being flexible, it's just not physically possible. For example, an air traffic controller hired to work a Saturday shift could be terminated if they subsequently refused to work on Saturday for religious reasons.
If this young lady had been hired as a singer and she was the only person in the entire establishment hired for that purpose then the situation would probably be different. But that doesn't appear to be what happened. This appears to be one of those establishments where the singing was a secondary job function performed by two or three of the hospitality staff when they were not busy with their primary responsibility --taking orders and serving food.