It would be exciting for the people in the choir to have the chance to sing. There will be former and current presidents there. The people in the choir will get to travel to Washington DC. They will receive publicity for themselves and for the Mormon church. It is a positive for everyone involved.
Setting aside any religious aspects that may be at play here, the purpose of the Tabernacle Choir's performance at the presidential inauguration is to honor the office of the President of the United States. It is not about supporting a single individual nor protesting him. The office, people often forget, represents the citizens of a nation that chose its inhabitant. In fact, honoring the office and position rather than a specific person is a part of (the Christian) religion and cancels out any personal feelings or religious beliefs about any particular government individual, at least in this instance.
The inauguration is an important part of the becoming of a president. If a choir sings at the inauguration the entire event will seem as though it is a fair, or a concert. Not a important coming of the president of the United States of America's next Head of State.
No, the Mormon Tabernacle Choir should not sing at Donald Trump's inauguration. The Choir is an honorable group of very talented singers whose purpose is to praise God and entertain the masses. Mr. Trump has shown himself to be a very offensive person whose ideals run counter to those taught by Jesus Christ.