The concept of charter school is very ambiguous. They get special funds for better school curriculum and practices and facilities. But they are not supporting a specific group of people who need that kind of facilities. It is unconstitutional to use general public's tax money to serve a certain group of children who are chosen by lottery. These funds should be equally distributed to all public schools.
No, it is not unconstitutional for Charter Schools to get property tax money. If these charter schools receive public funds, then they should no doubt receive property tax money as well. In fact, it is necessary to preserve and continue a good education at these schools - it is better for the students.
Charter schools are independent institutions of choice, created by individuals, families, or groups of a community. These institutions usually do not have to adhere to all of the same policies as a normal public school. Using this logic, it is reasonable to assume that these individual have decided against available public schooling. As an institution of choice it is I feel that it is unethical to use the same source of funding as a normal public school, while denouncing the available option of these public schools, potentially taking funds away from these school all the while adhering to only the rules of your choosing or agreement.
No, it is not unconstitutional for charter schools to receive property tax money because the funds are helping to further the education system, just as it helps public schools to prosper. Educational funding should not be limited to one type of school. All students deserve assistance and resources to improve their learning opportunities.