A recent article in Reuters, one that received a great deal of attention, sheds light on practices that some charter schools are using essentially to screen students who apply for admission. These policies include requiring long and difficult applications, family interviews, parental contracts, and even demonstrations of past academic performance.
It remains unclear how common these practices might be in the grand scheme of things, but regardless of how frequently they occur, most of these tactics are terrible, perhaps even illegal, and should be stopped. At the same time, there are two side points to keep in mind when you hear about charges such as these, as well as the accusations (and denials) of charter exclusion and segregation that tend to follow.
The first is that some degree of (self-)sorting and segregation of students by abilities, interests and other characteristics is part of the deal in a choice-based system. The second point is that screening and segregation are most certainly not unique to charter/private schools, and one primary reason is that there is, in a sense, already a lot of choice among regular public schools.