I've never been part of this "anti-testing crowd" until New York began botching things so badly. I was one of those people who kind of liked taking the SATs and GREs. I certainly believe there is a place for standardized testing.
Here in New York, however, flawed, secret tests have been rushed to development based on hurriedly written, unproven standards. These tests were then given multiple functions, far more than any single test should be asked to do: they supposedly assess students' strengths and weaknesses, provide districts with a "snapshot" view of their school, inform curriculum development and decisions, help disadvantaged students, punish failing schools, rate principals, fire failing teachers, place all teachers on an evaluation scale of ineffective/developing/effective/highly effective, and more. Then our governor stated that the scores on these tests are "meaningless" for students and should be viewed as "practice"--that's a scary mindset to place students in considering the high-stakes nature of the tests. In addition, it has been publicly pre-determined that a certain percentage of students WILL score below grade level and a certain percentage of teachers & schools WILL be labeled ineffective. These percentages are being set before the test is even administered!
Pearson closely guards the content of the tests, to the extent that 8-year-olds are required to sign confidentiality agreements, but multiple reports indicated that the NY tests contained many components that were several grade levels above the tested grade. A high percentage of students was unable to finish the timed tests. Then recently, when teachers were trained to score the tests, they reported that the "anchor papers" that were supposed to be written by students in the field testing stage did not contain high-scoring, student-written examples at the 5th grade level (possibly at other levels as well; this is the first report I've heard). The high scoring examples were written by the adults at Pearson, apparently because NO actual 5th grade child in the field test was able to successfully accomplish the assigned task.
I'm less familiar with other states, but my experience with the Opt-out movement in NYS is that the vast majority of participants are concerned parents who want their children to receive a rich and varied education. They are not anti-test. They allow and encourage their children to take the Regents exams and SATs, and those who have older children were fine with them taking the 4th and 8th grade assessments that had been in place for many years. They are, however, extremely worried about the use of our children as political pawns in the war on public education that has been declared by the governor and his rich backers.