To oversimplify, the Southern Baptist Convention has been going steadily more conservative since the Resurgence began. In 2000 the SBC modified its statement of faith, the Baptist Faith and Message. Since then the main controversy has been over the modification, and over the International Mission Board (IMB.org) having its missionaries all sign a paper saying they agree with the BF&M. In 1991 the Cooperative Baptist Fellowship split off of the SBC (http://www.thefellowship.info/); from all appearances the CBF is rather liberal, and as a matter of fact a very contentious point lately has been the CBF joining the Baptist World Alliance. Most opposition to the SBC and the IMB comes from within the SBC. The biggest single unit of opposition could be the Baptist General Convention of Texas.
Members of the BGCT have often criticized the SBC. Although there is some disagreement among Baptist over the SBC's and BF&M's stance that women should not be pastors, by far the most important division is over the 1963 BF&M's statement that the Bible is to be interpreted by Christ; and the 2000 BF&M's statement that the Bible is a testimony to Christ. A leader of this disagreement with the SBC is Dr. Jim Denison, the pastor Park Cities Baptist Church here in Dallas (Dr. Cook, president of DBU, is a member of PCBC) and one of DBU's trustees, as well as a past and new professor at DBU (starting this spring teaching systematic theology for a new master's program); Dr. Denison speaks in chapel every now and then. (Here is an article written by Dr. Denison on the subject.) "Conservatives" and "fundamentalists" say that making Christ the rule for interpreting Scripture opens up the Bible for subjective interpretation. In the above article you'll Dr. Denison (is he conservative, moderate, what? He sounded conservative in chapel recently, but he always takes the position of the moderates!) saying that it is an important principle for interpreting Scripture (hermeneutical principle) that Christ is the interpretation of Scripture.
Do you see why "conservatives" say this is a slippery slope leading to complete relativism? Who decides which part of the Bible corrects which part? Since it says so many things, what stops me from just picking the part I like and not the part I don't like?
Anyways, I think it was in 1998 that the SBC added to the Baptist Faith and Message a sentence or two about how only men can be pastors. The BGCT complained enough that some of them broke off and formed the SBTC.
The arguments over female pastors is one of the most important Baptist divisions these days.
Anyways . . . that's also been a huge issue.
The BWA president, Billy Kim, is a close friend of DBU. The Baptist Standard and Dr. Cook have been saying a lot about the need for Texas Baptists to support the BWA. It really looks like the BGCT is planning on pulling away from the SBC altogether sometime in the future. Not this year; could be not for a long time.
Tell the rich old ladies who give money to DBU that Dr. Denison, most regular chapel speaker, trustee, Dr. Cook's pastor, and professor for Masters level theology courses denies the inerrancy of Scripture, DBU will suddenly have serious financial problems.
I will now make biased comments. While it is certainly true that Jesus Christ is the "criterion" for interpreting Scripture, this is only so as a subset of the hermeneutical principle that the New Testament interprets the Old Testament (though the OT is vital for understanding the NT, as a background).
What if we only had this principle of interpretation? We'd interpret the Bible by Christ...how would be know who Christ is? So the more fundamental principle is that the Bible reveals who Christ is.
The so-called conservatives and fundamentalists emphasize the historic Baptist position, that Scripture is inerrant. The so-called moderates emphasize what they say (for all I know, this is correct) is the historic Baptist doctrine of the autonomous church, and the autonomous believer (which is why missionaries having to sign the BF&M would be wrong). The Baptist position on Scripture is the also the orthodox Christian position. Dr. Denison apparently feels that it's more important to have the Baptist autonomy than the historic Baptist doctrine of Scripture. I disagree.
Here are some of the more important links:
SO-CALLED MODERATE STATE CONVENTION, WITH WHICH DBU IS ALIGNED
SO-CALLED FUNDAMENTALIST STATE CONVENTION
MODERATE CONVENTION'S NEWSPAPER
FUNDAMENTALIST CONVENTION'S NEWSPAPER
NEWS FROM THE NATIONAL CONVENTION
This article was kind of interesting. Romanian guy vs. Dr. Cook.