Under the Federal Equal Access Act, any school that receives government funding and has at least one other non-curricular club must also allow a GSA. As the law states, “It shall be unlawful for any public secondary school which receives Federal financial assistance…to deny equal access or a fair opportunity to, or discriminate against, any students who wish to conduct a meeting …on the basis of the religious, political, philosophical, or other content of the speech at such meetings.”
The law also says that your school must treat all clubs the same and let them use school resources in the same way. If your school allows other clubs to meet in classrooms, put up posters and organize school events, then they have to allow your GSA to do the same.