Florida is a "closed primary" state. Which means:
If you wish to vote in a partisan primary election, you must be a registered voter in the party for which the primary is being held. (Section 101.021 Florida Statutes)
However, if all candidates for an office have the same party affiliation and the winner will have no opposition in the general election, all qualified electors, regardless of party affiliation, may vote in the primary election for that office. Also, all registered voters, regardless of party affiliation can vote on issues and non-partisan candidates.
If there is opposition and you are registered as "no party affiliation" or with a minor political party, you can only vote for:
"Nonpartisan candidates and Issues only"
County Judges and School Board Members are Nonpartisan Candidates