Regulation of schools is the job of state governments in the United States by default. Political forces in the state legislature in Texas make it hard to fix this problem solely by state legislation, because the Responsive Ed curriculum does represent the point of view of some highly motivated and politically active Texas voters. The article author points out that federal constitutional principles ban teaching religious doctrine in the guise of teaching school curriculum content, so that is one possible response to the skewed curriculum in these charter schools. Another, too little considered in most articles about school choice in general, is simply for other schools to boldly proclaim that their curriculum is better, and explain why it is better. The Responsive Ed schools surely find agreement among some parents shopping for schools in Texas, but they would also be embarrassed to have to defend point by point all of the ridiculous things they say in their curriculum. In particular, it would be good for other schools to specifically mention the many lines of evidence for macroevolution[1] as they promote their curriculums. Comparative advertising is still an under-used tool for promoting school reform, even in states like mine with pervasive public school open enrollment.
I think John Stuart Mill got the policy balance correct more than a century ago, when school attendance was not compulsory in Britain nor in most parts of the United States: "A general State education is a mere contrivance for moulding people to be exactly like one another: and as the mould in which it casts them is that which pleases the predominant power in the government, whether this be a monarch, a priesthood, an aristocracy, or the majority of the existing generation in proportion as it is efficient and successful, it establishes a despotism over the mind, leading by a natural tendency to one over the body."
John Stuart Mill On Liberty (1859)