The Mormon Tabernacle Choir isn't protesting performing at Trump's inauguration, one member just decided not to sign up for it and made a statement about it.
Regardless, they should perform at the inauguration, it only makes sense to. No one should be so vividly against performing just because of their political views. Celebrities need to realize they are not God's gift to the world, suck it up, and perform.
Yes, the Mormon Tabernacle Choir should perform at Trump's inauguration, if they choose. Being asked to perform at a Presidential Inauguration is a great honor and responsibility, regardless of whether you agree with the individual taking the position. The choir is famous and has been asked to perform at many key events. They may feel they can help to bring some unity to our country by participating.
There are people who see the performance as political, but the truth is that the choir has performed for many inaugurations. The performance is not a show of support for the election of Trump, specifically. Rather, the choir is just showing support for the United States. Mormons have a proud history and legacy in the United States, so their participation is worth celebrating.
In a modern multicultural society, I think it is better if religion and politics are kept as far apart as possible, regardless of how controversial the president is. If you can't include everyone, then you must exclude everyone in the name of equality and only have non religious performances, otherwise it sends the wrong message.