Professional baseball's growth in the United States was different from the growth in Latin America in one specific, important aspect: United States players had to face the color barrier:
The National Association of Base Ball Players was formed in 1857 as a way to "promote the standardization of playing rules, to regulate inter club competition and to encourage the growth of baseball." This association expanded throughout the U.S., causing members to take professionalization and the color line into consideration (Burgos, p. 21).
Also known as the National Association, the organization suffered many obstacles when it established the color line. Specifically, professionalization would open the sport to everyone, no matter what race or color. The association feared that as a result, "rowdies, drunkards, and dead-beats" would be drawn to these games, reducing the character of the game (Burgos, p. 22-23). In addition, gambling issues were relevant, as players would throw games away for additional income, ultimately destroying the National Association's reputation.
The National League was established in 1876 as a result of the destruction of the National Association. The National League's function was to manage baseball teams. In addition, clubs would form leagues, make schedules, and pay salaries to players. The reason behind this was to require full effort from players, eliminating gambling (Burgos, p. 26-27). However, the color line was evident in a sense that it limited the talent that teams could acquire from the minor leagues (Burgos, p. 29).
http://www.wbur.org/onlyagame/2015/07/11/latino-baseball-history
From Cuba To Cooperstown: The History Of Latinos In Baseball
Baseball's color line would remain firmly in place from 1889-1946. Because of the color barrier, the Negro League was formed. Many African Americans, as well as around 10-15% of Afro-Latin Americans played in the Negro League (Johnson and Rosario). In 1900, Cuban teams competed against Negro League teams in exhibitions in Havana, and what followed was Latin Americans going to the United States to play in the Negro Leagues. In addition, Negro League athletes such as Jackie Robinson and Satchel Paige would play in leagues in Latin American countries ("From Cuba to Cooperstown: The History of Latinos in Baseball").
From Cuba To Cooperstown: The History Of Latinos In Baseball
During World War II, American baseball players were called to serve, causing many Latinos to fill vacated roster spots. Participation continued to be limited to light-skinned Latinos, however, until 1947, when Jackie Robinson became the first African American to play in the U.S. major leagues. This ended the color barrier and paved the way for dark-skinned Latinos to play professionally in the U.S. ("From Cuba to Cooperstown: The History of Latinos in Baseball").