Final answer:
The rise of socialism is not directly linked to the question's options related to race relations in the U.S.; rather, the correct answer involves key legislation from the Civil Rights Movement, which improved race relations by ending segregation and securing voting rights.
Step-by-step explanation:
The question regarding how the rise of socialism affected race relations in the United States seems to be conflating different historical issues. Socialist movement, as a class-based ideology, does not directly correlate to racial relations as described in the provided options. Instead, the question likely refers to broad social and political movements and legislation that impacted racial dynamics.
The correct answer regarding historical events that most closely aligns with the provided choices is option E, "It led to legislation that resulted in African Americans gaining the right to vote in elections." This aligns with the historical efforts of the Civil Rights Movement, which is better represented by legislation such as the Civil Rights Act of 1964 and the Voting Rights Act of 1965. These laws were significant landmarks in improving race relations by ending legal segregation and ensuring voting rights for African Americans.