Final answer:
The Supreme Court case Smith v. Allwright ruled that white primaries were unconstitutional. This decision in 1944 ensured African Americans the right to vote in primary elections, marking progress in the fight against de jure segregation.
Step-by-step explanation:
The court case that deemed white primaries unconstitutional was Smith v. Allwright. In this landmark decision, the Supreme Court struck down the practice of allowing only white individuals to vote in primary elections. Lonnie Smith of Houston sued local election official S.S. Allwright after being denied the right to vote in the Democratic primary of 1940. Despite arguments from the Democratic Party of Texas that it was a private organization and thus exempt from the Fifteenth Amendment, the Supreme Court ruled that primary elections were state-regulated and must not racially discriminate. This decision played an instrumental role in ensuring the right to vote for African Americans in primary elections and was a significant step towards ending de jure segregation.