Overwhelmingly, the oot out movement was pushed by white parents who were afraid that their children's test scores would not live up to their inflated grades. This was especially true after states adopted the more rigorous common core state standards (CCSS) which replaced many states standards which expected far less from students.
At the high school level, down to 8th grade the CCSS were based on decades of research by The SAT and The ACT on what skills students who were successful in college were able to do. It used the PSAT and lower grade ACT tests (EXPLORE and PLAN) to back map those skills to tenth and eighth grade. Further back mapping of the CCSS was based on published research on teaching skills and things like learning trajectories and learning progressions.
There were two parts to the push back on CCSS. There was the thinly veiled racist attacks from the far right (Obama core)-- which was spit out with such vitriol that it wasn't hard to hear the implied n-word at the beginning. This was where a lot of the opt out movement came from.
The second part was from policy folks who opposed the use of standardized tests to make funding decisions. One if the bad consequences of NCLB and it's follow up ESSA is that schools that perform poorly on standardized tests can be penalized by losing funds. The same law allowed extra money to go to schools and school districts that scored well. This was the worst and most problematic part of those laws. We know that test scores are highly correlated to average family income in a district, not because the tests are biased but because of societal factors. Children from homes with middle class income and at least one college educated parent enter school knowing tens if thousands more words than children from a family near the poverty line. There is also the access to opportunity to learn gap. Middle class families can afford to take their children to museums, zoos, libraries, etc that help the kids learn a lot of stuff before school. Sadly, the research shows that the gap widens with increased schooling usually.
Back to grade inflation. When I started teaching in the mid 90s, the average HS GPA was about 2.7. now that average is about 3.5. Are kids really a letter grade better than they were 25 years ago? This is where standardized test scores come in. They give a fair and equal measuring stick for all students.
Research shows that grade inflation is more prevalent the higher percentage of white and Asian students in a school. The more BIPOC students, the less grade inflation and the lower the average GPA, even for schools with equal standardized test scores. So, removing standardized testing actually codifies the higher position of traditionally served students (whites and Asian) and harms black, Latino, mixed race, and indigenous students.
If white students opt out, we don't see the man behind the curtain, helicopter parents who bully schools, teachers, and school boards for higher grades.
The systemic problem of using test scores for funding needs to be addressed. But opting out only allows suburban (studies above with white and Asian kids and grade inflation) kids to hide behind inflated grades and not prove what they know and can do.