Although it's not clear how such information obtained by schools would actually be used, one can imagine some of the consequences it might have. It could lead to some students whose families have questionable immigration status being denied entry to our schools. On one side of the debate, if there are students in our educational system whose parents are in the country illegally, with the financial straits and lack of resources plaguing our schools nationally, why should those parents be rewarded with the guarantee of a free public education for their kids? Taking it a step further, these students are eating up precious funding and resources that otherwise would benefit children whose parents are legal. You could see how this might affect special education as well - think of the dollars that could be put toward special ed if that money wasn't funding the education of children whose parents were never legally admitted to the U.S.
On the other side, those children whose parents came here illegally, did not take part in that decision and shouldn't be punished for their parents' actions. First of all, those children who were born in the U.S. are American citizens anyway, regardless of their parents' immigration status, and therefore are entitled to the same rights as any other citizen. What about those children who were not born here but were brought over by their parents illegally? I am not an expert in immigration law, but the NY Times article seems to suggest that a 1982 U.S. Supreme Court decision addressing that issue held that states could not withhold funding for or deny entry to children of illegal immigrants because those kids were not responsible for their immigration status.
The immigration debate is a heated one, for sure. How Section 28, specifically, will affect education locally and in other states remains to be seen. If nothing else, this story demonstrates the tension that exists between federal and state government on the issue of immigration, each trying to influence legislation that could have significant ramifications for the country as a whole.