Because of federal law and First Amendment jurisprudence, it is very difficult for a school to discriminate against the formation of a Queer/Straight Alliance. There are two main sources of law which the denial of the formation of a QSA are challenged under: the Equal Access Act,20 U.S.C. § 4071, et, seq. and the First Amendment. The Equal Access Act prohibits public schools from discriminating among noncurriculum related student clubs based on their speech content.
In plain language, if a school allows one noncurriculum based club to meet, they cannot deny any other club from meeting based on the content of the clubs speech. More specifically, the EAA was essentially created by a conservative Congress to make sure that religious based clubs would be allowed to use school resources to meet, however, the openness requirement has proven to be advantageous to QSAs claiming a right to meet. Essentially if a school receives federal fund and maintains a limited open forum (a term of art under the EAA, not to be confused with the similar term of art under the First Amendment of a limited public forum), a school cannot deny equal access to its facilities based on speech content. In order to prove a limited open forum under the EAA a plaintiff needs to find only one noncurriculum based club/organization to meet on school grounds. 20 U.S.C. § 4071(b) (2006).
It is unclear how exactly the EAA and the First Amendment differ in this area, but under the First Amendment, one must first do a forum analysis.
The forum analysis is used as a means of determining when the government’s interest in limiting the use of its property to its intended purpose outweighs the interest of those wishing to use it for another purpose. Cornelius v. NAACP Legal Def. & Educ. Fund, Inc., 473 U.S. 788, 800 (1985). The initial step in a First Amendment analysis is to determine the type of forum. Id. In Arkansas Educational Television Commission v. Forbes, 523 U.S. 666 (1988), this Court outlined three types of public forums: the traditional public forum (streets and parks), the public forum created by government designation, and the nonpublic forum. 523 U.S. at 677. A school will never be a public forum, which has the greatest protection for free speech. Thus the question in regards to a school is whether they have created a designated public forum/limited public forum or whether they have restricted access to the school in such a way as to maintain a nonpublic forum.
When the government has intentionally designated a place or means of communication as a public forum, speakers cannot be excluded without a compelling government interest. Cornelius, 473 U.S. 788, 800 (1985). In Hazelwood School District v. Kuhlmeier, 484 U.S. 260 (1988), the Supreme Court reiterated that school facilities may be deemed public forums only if school authorities have "by policy or by practice" opened those facilities for indiscriminate use by some segment of the public such as student organizations. If the facilities have instead been reserved for other intended purposes, "communicative or otherwise," then no public forum has been created, and school officials may impose reasonable restrictions on the speech of students. Hazelwood School District v. Kuhlmeier, 484 U.S. 260 (1988).
Under a First Amendment analysis, the school's policy for allowing organizations to meet at school will be scrutinized. If the policy generally allows student organizations to meet with little or no connection to curriculum, or if they encourage the creation of student organizations, they will have created a limited public forum and then they will have to establish that the reason the rejected club was denied serves an important government objective and is narrowly tailored to meet that requirement (it's essentially an intermediate review constitutional analysis).

Below are some relevant cases discussing student speech rights, the EAA, the First Amendment, or QSAs.

Federal Cases

Arkansas Educational Television Commission v. Forbes, 523 U.S. 666 (1988)

Bethel Sch. Dist. No. 403 v. Fraser, 478 U.S. 675 (1986) - Important First Amendment Case

Board of Education of Westside Community Schools v. Mergens, 496 U.S. 226 (1990) - Important EAA case

Boyd County High Sch. Gay Straight Alliance v. Bd. of Educ., 258 F. Supp. 2d 667 (E.D. Kan. 2003)

Caudillo v. Lubbock Indep. Sch. Dist., 311 F. Supp. 2d 550 (N.D. Tex. 2004).

Cornelius v. NAACP Legal Def. & Educ. Fund, Inc., 473 U.S. 788, 800 (1985)

East High Gay/Straight Alliance v. Bd. of Educ. of Salt Lake City Sch. Dist., 81 F. Supp. 2d 1166 (D. Utah 1999)

Gay-Straight Alliance of Okeechobee High Sch. v. Sch. Bd., 483 F. Supp. 2d 1224 (S.D. Fla. 2007)

Greer v. Spock, 424 U.S. 828 (1976)

Hazelwood School District v. Kuhlmeier, 484 U.S. 260 (1988)- Important First Amendment Case

Lawrence v. Texas, 539 U.S. 558 (2003)

Morse v. Frederick, 127 S. Ct. 2618 (2007) (also known as the Bong Hits for Jesus Case)

Perry Education Association v. Perry Local Educators' Association, 460 U.S. 37 (1982) - Important First Amendment Case

Pope v. E. Brunswick Bd. of Educ., 12 F.3d 1244 (3d Cir. 1993)

Shanley v. Northeast Indep. Sch. Dist., Bexar County, 462 F.2d 960 (5th Cir. 1972)

Tinker v. Des Moines Indep. Cmty. Sch. Dist., 393 U.S. 503 (1969)- Important First Amendment Case

Vernonia Sch. Dist. 47J v. Acton, 515 U.S. 646 (1995)

Widmar v. Vincent, 454 U.S. 263 (1981)- Important First Amendment Case