If they are supporting LGBT then it isn’t much of a “Church of Christ”. The Church of Christ follows the New Testament as closely as possible and buggering and clambumping isn’t condoned.
Hence the differentiation between Churches of Christ and the United Church of Christ, which went apostate many years ago.
One is a network of independent churches that strive to preach the Word of God, and the other might be more aptly referred to as a 'social club with a cross on the building.'