In the case of the SBC, you have a central authority, controlling local churches.
That is not Christian, since the local church is suppose to be independent.
No. You are 100% wrong. That would be the Catholic church, maybe the Episcopalians, I don’t know, Jehovah’s Witnesss (well, they’re not Christian anyway), and a slew of others.
EVERY, EVERY SINGLE Southern Baptist church, EVERY 0NE is totally independent of any outside authority. The Southern Baptist Convention is composed of churches that voluntarily associate with it, as are all the State conventions, and county associations. They do this in order to more efficiently witness, to support misssionary work, to produce Sunday School lessons, etc.
But each is independent, can withdraw at any time and join another Baptist convention, or none at all. If they stay, they are NOT bound by whatever the convention or its officers say. The SBC speaks only for itself, and not for any of its members.
But while they have no power, or authority over its churches, they may, or may not have some influence over some, only some, of them.