Mississippi has nonpartisan registration. There is no option to affiliate with a political party on the voter registration form.
Details of voting in congressional and state primary elections:
Voters do not declare affiliation with a party in order to vote, but they must choose one party's ballot.
Voters who choose to vote in the Democratic Party primary must "intend to support" the Democratic Party's nominee in the general election. Voters who choose to vote in the Republican Party primary must "intend to support" the Republican Party's nominee in the general election. However, the Supreme Court has ruled there is no legal way to enforce this.