Q:

What is the Baptist justification for anti-confessionalism?

According to Wikipedia, "Confessionalism, in a religious (and particularly Christian) sense, is a belief in the importance of full and unambiguous assent to the whole of a religious teaching. Confessionalists believe that differing interpretations or understandings, especially those in direct opposition to a held teaching, cannot be accommodated within a church communion."
So, the main question is this: what is the Baptist justification for anti-confessionalism?
Baptists are one group that may be anti-confessional.

A:

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:

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.'
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...

