The term that describes only white people being able to vote in the primary party elections, so they decided who would be running in the regular election

White Primaries.

Explanation:

The primary was an election held within a political party to nominate the person for public offices. In the 1920s, Southerners used a legal device of 'white primaries' to restrict the voting rights of African Americans. This device, along with, many other devices were used by white southerners to restrain the former slaves from exercising their political, economic, and social rights.

This primary political election was renamed as 'white primary' as it curbed the voting rights of any other race. It was also a tactic of the Democrats to weaken the Republican political party as the party consisted mostly of black members. So, white primary lowered the influence of the Republicans in the South by enacting a law of white primary.

So, the term is the 'white primary.'