Only quirk I know of {if it’s still that way} is no musical instruments allowed at services.
Like most sects, the Church of Christ (not the UCC) is convinced that it alone is the true Christianity, but at least they don't burn everyone else as heretics.
The no-musical-instruments, however, hearkens back to the time of Ambrose: it was a compromise between those who wanted music in the church because the Bible says so, and those who didn't want music in the church because the music of the late Roman Empire was associated with activities as raunchy as those for which most popular music is associated today. By removing the instruments, Christians wouldn't be giving the impression that they approved of raunchiness, but by singing their praise, they would be fulfilling God's command.