I really don't think it has to do with the Jewish population in Florida. First off the state is 70% Christian and only 3% Jewish, but northern Florida is a southern state. Most of the liberals are in the southern tip of the state (Miami area) and the rural areas tend to be demographically similar to the rural areas of other southern states.
In the US there are more people registered Democrat than Republican, but Democratic voters tend to be less reliable. Republican voters tend to be older and whiter, two demographics who tend to vote in off year elections. There are 36 states that have their gubernatorial elections in off years (non-presidential election years), 12 that have them in presidential election years, with 2 that do it in odd numbered years. Turnout in non-presidential election years is always lower than presidential elections and the more reliable voting demographics have more sway in those off years.
In 2010 the Republicans developed a deep strategy to take over as many state governments as possible. Because they had more conservative voters turning out anyway, extra effort put a lot of Republicans in office in a lot of states. This included governors, other statewide offices, and legislatures. After the results of the 2010 census came in and it came time to redraw districts for elected offices in both legislatures and Congressional districts, these Republican majority legislatures drew up district boundaries that were easier for Republicans to win and harder for Democrats.
With control of the legislatures Republicans were able to rig the elections to favor turnout for Republicans and make it harder for Democrats to vote. This included voter ID laws that allow ID Republicans are more likely to have like concealed carry permits, but not allow ID Democratic voters might have like school ID cards. They also rigged things to make it harder to get IDs in areas that tend to vote Democratic (closing DMVs for example), have fewer polling places per capita in areas that vote Democratic, and purged voting rolls of names who might be dead or felons, though tend to concentrate on people who live in more Democratic areas.
Back many years ago, Democrats were known to play similar games to discourage Republican voting. The era of the poll taxes and literacy tests in the South were during a time when the white Democrats controlled things and African Americans tended to vote Republican. The Democrats in Chicago were also know to put their thumb on the scale in various ways.
But in the last 25 years or so, the numbers are on the Democrats side. When turnout is high, Democrats tend to win and when it's low they often lose. When California redistricted using the system used by Washington State for the 2012 election (which redistricts using a bipartisan commission and districts have to be along normal boundaries), California's Congressional delegation and state legislature got more Democrat.
Florida was one of the states that the Republicans gained seats in Congress and in the state legislature as well as statewide offices. Since then the thumb has been on the scale to favor Republican candidates.
Florida is a very diverse state. There are sharp differences in political views between regions of the state and other demographics. Cuban-Americans have been a reliable Republican voting block for 60 years because Kennedy was in office during the Bay of Pigs (though the plan was developed during the last days of the Eisenhower administration). Younger Cuban-Americans are less likely to vote Republican, though I think they still vote more Republican than other Hispanic groups. Like a lot of states, the cities are more liberal than the rural areas, but Florida has a fair bit of the state is rural and conservative.
In short, it's complicated.