The issue is that if a charter school receives federal/state funds, they can't really discriminate against children. They can't refuse to take disabled kids. What if they then said, we won't take kids with learning disabilities, or kids who don't speak English well, or kids who are African-American... etc. It becomes a slippery slope. If the tax payers are paying for the school, they do not have the right to discriminate against some kids and refuse them entry into the school.
Children with disabilities are protected by federal laws. They are entitled to receive a public education that places them in the least restrictive environment where they can learn.
Ok, but look at the Basis charter schools of Arizona. Their high school curriculum page
https://www.basisschools.org/index.php?option=com_content&view=article&id=92&Itemid=103 says
"BASIS Upper School offers an accelerated liberal arts curriculum that is among the most sound and rigorous in the country; a curriculum that asks students to work hard to reach their academic potential; and that offers the assurance of comprehensive benchmarking and expert teaching. It is a curriculum that holds students accountable for their own success; that fills in them a deep reservoir of knowledge; and challenges them to think creatively about that knowledge. It is a curriculum that arouses the confidence to engage intelligently with the world around them.
The curriculum for grades 9 through 11 is centered on the College Board's Advanced Placement program in all core subjects. Students must take at least six AP exams and eight AP courses throughout their high school tenure, with these exams counting as Final exams in the course and comprising part of a Board Examination system. All BASIS graduates complete an AP course in each of the core disciplines: English, math, science, and social science."
Pass six AP exams to graduate from high school!
In a recent thread I have cited a study showing that PSAT scores predict AP scores. In other threads I have argued that the SAT (and thus the PSAT) is largely an IQ test. Scores on AP tests, SATs, and IQ tests all show similar patterns. Students and parents look at graduation requirements and avoid the school if they think it is too demanding.
The Basis charter in Scottsdale, AZ
http://www.publicschoolreview.com/school_ov/school_id/118950 is 0% American Indian, 33% Asian, 3% Hispanic, 1% Black, and 64% White. Arizona is 9% American Indian, 2% Asian, 27% Hispanic, 6% Black, and 41% White.
Kids who are LD or ELL are likely under-represented also.
If charter schools are free to set their own academic standards, this can result in a very different demographic mix than the surrounding area, without any explicit discrimination.