ARBCA and FIRE are both associations of churches that have plurality elder rule leadership.
FIRE refers to the 1646 and 1689 Baptist Confessions, but does not require strict adherence. Here is a quote from the FIRE confession of faith on the church:
[quote:56c9243109]We believe that the local church is under the authority of Christ alone. Nevertheless, He has appointed men to be elders (undershepherds) to represent Him as they care for His body. Deacons also serve Christ as His ministers of mercy. Furthermore, the communion of saints requires the recognition of and fellowship with other local evangelical churches.
http://www.firefellowship.org/confession.htm[/quote:56c9243109]
And ARBCA requires strict adherence to the 1689.
[quote:56c9243109][i:56c9243109]1689 on the Church[/i:56c9243109]
The Lord Jesus Christ is the Head of the church, in whom, by the appointment of the Father, all power for the calling, institution, order or government of the church, is invested in a supreme and sovereign manner; neither can the Pope of Rome in any sense be head thereof, but is that antichrist, that man of sin, and son of perdition, that exalteth himself in the church against Christ, and all that is called God; whom the Lord shall destroy with the brightness of his coming.
To each of these churches thus gathered, according to his mind declared in his word, he hath given all that power and authority, which is in any way needful for their carrying on that order in worship and discipline, which he hath instituted for them to observe; with commands and rules for the due and right exerting, and executing of that power.
A particular church, gathered and completely organized according to the mind of Christ, consists of officers and members; and the officers appointed by Christ to be chosen and set apart by the church (so called and gathered), for the peculiar administration of ordinances, and execution of power or duty, which he intrusts them with, or calls them to, to be continued to the end of the world, are bishops or elders, and deacons. [/quote:56c9243109]
Some SBC churches have adopted elder rule, but they are far and few between.
Phillip