"We oppose the teaching of Higher Order Thinking Skills (HOTS) (values clarification), critical thinking skills and similar programs that are simply a relabeling of Outcome-Based Education (OBE) (mastery learning) which focus on behavior modification and have the purpose of challenging the studentâ(TM)s fixed beliefs and undermining parental authority."
We shouldn't challenge student's fixed beliefs? Or undermine parental authority? Those sound like usual and desired outcomes of critical thinking skills.
In order to apply critical thinking skills, however, you have to establish a corpus of information (knowledge) from which to operate as a base when testing new information for validity.
In other words, you can't start from a phenomenological basis from the start, you have to assume language in order to be able to communicate about concepts, and then adequately judge their validity or invalidity.
What this means is that you have to shovel their heads full of as much rote knowledge as you can possibly shovel in, prior to their critical thinking filter slamming into place and interfering with the process o communicating things like "rules of grammar", "mathematical concepts", "tigonometric identities", and so on. Because once those filters slam into place, they are going to be thinking for themselves, and so busy questioning the validity of what an authority is saying, and their motives for saying it, that it's going to be difficult to jam anything in.
As to the validity of the rote knowledge you've already jammed into their heads prior to that event - effectively, where they stop being sponges, and wake up into themselves as human beings - well, hopefully the event that throws up the gates occurs after you have taught them Aristotelian logic, and Platonic/Homeric introspective self examination ("The unexamined life is not worth living"), so that they can selectively filter for any "bullshit" that was inserted, along with their times tables or the idea that sin(x) + cos(x) = 1.
So while their motivations may be impure, I have to agree with them that, at least through High School, you want to just shovel as fast as you possibly can, and then when they get to their Sophomore year in college, you send them to the philosophy department to teach them symbolic logic, and you send them to the physics department to teach them how to think rationally about problem solving (something physics is good at, because it's as unforgiving about facts as gravity in a "Road Runner" cartoon isn't).
And if they never make it to their Sophomore year in college, because they stop after the mandatory public schooling, and don't pursue further education... well, they will likely be happier as people not having had their delusions challenged, particularly since those delusions were probably shoveled into their heads at a young age - say 5 or so - and all you are going to do by having taught them critical thinking skills early is to make them miserable as adults.