I believe this is a misunderstanding, and one similar to the misunderstanding some would apply to creeds and confessions.Some people reject creeds and confessions because of their content. They do not want to be pinned down as to what they believe. They want the option to move the goal posts if necessary.
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I have never encountered anyone who rejects creeds and confessions because they want to hold flexible doctrine (this does not mean you are wrong but it is why I believe that to be the case). Often the issue is more that people do not want to be pinned down to a creed or confession but they are willing to be pinned down to the Scripture behind those things.
Creeds and confessions work to unite, to bring together, or to explain to the group to which they apply the beliefs of a whole.
Where they fall apart is when they are imposed upon people who do not hold them as some type of authority.
The danger that I have seen is in the misuse of these things. I have seen doctrine defended not on the grounds of Scripture but on the grounds of a particular creed. This is indoctrination, not biblical edification.
I can argue a group should not belong to the SBC by presenting the SBC F&M. I can say "here is what I believe" and offer the same. But I should not insist another affirm the confession or that it is itself an authority for my faith.