To them it is not pedantic. Having learned the history of the name change, they explicitly left out "the" in their name. To them they were called to be a Community of Christ and not The Community of Christ. The distinction means a great deal to them. Using "the" to begin a sentence followed by the name is a waste of time.
Example...
"Community of Christ officially changed its name 1 January 2001."
Vs.
"The Community of Christ officially changed its name 1 January 2001."
The two sentences do not have the same meaning. There is absolutely a distinction with a purpose.
Consider it in terms of the LDS church. Perhaps dropping "the" at the beginning of the name is pedantic.
Example again...
The Church of Jesus Christ of Latter-day Saints
Vs
Church of Jesus Christ of Latter-day Saints
Vs
the Church of Jesus Christ of Latter-day Saints
To LDS people there is a clear distinction between the three. Perhaps you're right and people are being pedantic.