What is the Baptist justification for anti-confessionalism?

Yes, Baptists have a very different view of authority than, say, Catholics. Baptists believe that it is the right and responsibility of every Christian to study the scripture for himself, rather than accepting some set of beliefs promulgated by an authority.

Baptists point to Scripture passages such as:

Acts 17:11 "These [the people of Berea] were more fair-minded than those in Thessalonica, in that they received the word with all readiness, and searched the Scriptures daily to find out whether these things were so." People are praised for studying the scriptures for themselves to see what is true and what is not.

1 Peter 2:7,9 "Therefore, to you who believe ... you are a chosen generation, a royal priesthood, a holy nation," Peter is addressing all believers, and calls them "a royal priesthood". From this Baptists get the doctrine of "the priesthood of the believer": we are all priests, not just a select few.

Romans 14:3-6,10 "Let not him who eats despise him who does not eat, and let not him who does not eat judge him who eats; for God has received him. Who are you to judge another’s servant? To his own master he stands or falls. Indeed, he will be made to stand, for God is able to make him stand. One person esteems one day above another; another esteems every day alike. Let each be fully convinced in his own mind. He who observes the day, observes it to the Lord; and he who does not observe the day, to the Lord he does not observe it. He who eats, eats to the Lord, for he gives God thanks; and he who does not eat, to the Lord he does not eat, and gives God thanks. ... But why do you judge your brother? Or why do you show contempt for your brother? For we shall all stand before the judgment seat of Christ." Paul discusses some debates then going on in the church, like whether it was appropriate to eat meat that had been sacrificed to idols, and whether Christians should celebrate the Sabbath. And he concludes: each Christian must decide such questions for himself, and not judge those who came to different conclusions.

In theory, at least, if in a meeting of Catholics someone said, "I disagree with the Pope about this", other Catholics would tell him that he must be wrong: the pope's statements on doctrine are infallible and all Catholics must accept them. If in a meeting of Baptists someone said, "I disagree with the president of our denomination about this", other Baptists would say, "Oh? What verses can you point to to defend your position?"

Of course like any general principle, there are limits to how far Baptists take this. We consider some beliefs to be fundamental, and if you don't accept those, we don't deny that it is your right to believe that way, but we do deny that you have any reasonable basis to call yourself a "Baptist". Like if you deny that there is a God, or that Jesus died for our sins, or that there are such places as Heaven and Hell. (Just like, Libertarians say they believe in free speech. You can say whatever you want. But if you say that you don't believe in free speech, they won't agree to call you a Libertarian. Etc.)

Baptists*, in particular, are fond saying "We have no creed but the Bible." As this wonderful video shows, that is a creed, but it gets to the heart of your question - why do Baptists view creeds negatively? [Really - go watch the video. It does a better job than I will of explaining the reasoning, and debunking it!]

There is one scriptural reason and one legacy:

1. Baptists have a very particular notion of 'vain repetitions' as used by Jesus in Matthew 6:7. Even the Lord's Prayer or the liturgy--anything that smacks of 'saying the same words without any meaning behind them'--is taught against regularly in Baptist teaching. As such, there tends to be a distrust of anything liturgical. Along those lines, some will also add Paul's bit about some following Paul, others Apollos, and other 'Christ.'

2. The simple fact of the matter is that 'credalism' or 'confessionalism' as you prefer to put it, is really a mask for a greater issue - namely, Baptists have a very significant distrust of Roman Catholicism. This distrust has historical roots and is often taught using the concept that 'traditions' are less 'good' than scripture. (We won't get into the fact that how one reads scripture is a tradition.) This manifests itself in the 'Trail of Blood' rhetoric and has a long pedigree.

As you can see, even as a Baptist, I don't put much stock in these arguments, but they are deeply engrained in the teaching.

*Just to clarify, I'd suggest that a big asterisk go on "Baptists" here. This tends to be the view of an older, more fundamentalist strain of Baptistic thought than what is probably the mainstream today. I use the word here to denote what types of protestants are most likely to meet your criteria, moreso than to argue the point for the whole. That said, I don't have any numbers either...