That area actually does have a long history. There were several pre-Brown civil rights cases including some in Texas where state law in the primaries was overturned by the US Supreme Court on the grounds that it intentionally violated certain civil rights. I just emailed a friend to look for that arkansas case for me.
"The reason I heard from him was that under Arkansas state law he earned enough votes in the 2000 Democratic primary election to qualify for 7 delegates to the national convention (out of several thousand). The Chairman of the DNC, however, used an obscure party rule to decide that LaRouche wasn't "in sympathy with the ideals of the Democratic Party," thus depriving him of his delegates. After the Supreme Court ruled that political parties are private clubs that can exclude anyone they want to, LaRouche decided to send printed materials and videotapes to all Democratic delegates, alternates and pages in an attempt to get them to support the seating of his delegates. Needless to say, he failed." http://www.harvardindependent.com/news/2002/12/05/Forum/Lunatics.In.The.Pit-337266.shtml
It also looks like the Arkansas case went through the state level first as "LaRouche v Democratic Party of Arkansas" in 2000 under Pulaski County Circuit Court, Judge John Ward. Ward ruled against LaRouche even though Arkansas state law specifies "The Delegates to the national party convention shall be apportioned to the presidential candidates whose names were on the ballot at the primary, in the proportion that the votes cast for each candidate bear to the total votes cast." It appears that this is the case that was appealed to the federal level, which also ruled against LaRouche. I haven't found that case's name yet though.