Florida's first-year Republican governor, Bob Martinez, a recent convert to the GOP, is learning what being a Republican is about to some people. Shortly after his inauguration, Martinez, who campaigned on a good Republican promise to cut the state budget by $800 million, went out front favoring a 5 percent service tax, which took effect July 1. The tax is on legal and accounting services, real estate transactions, advertising, publishing and other business activities and is expected to raise about $1 billion a year.

It raised a furor in the business community and among Republicans who share President Reagan's disdain of tax increases. Tommy Thompson, a Panama City auto dealer and former state GOP chairman who ran all of Reagan's Florida presidential campaigns, told the people of Florida that he owes them an apology for helping convert and elect Martinez.

"I'm not sure he knows what a Republican is," the flamboyant Thompson fumed. "We brought him in and baptized him as a Republican and then he gets out front for a tax that's the brainstorm of the Democrat legislators. Any good conservative could cut $800 million there in Tallahassee, starting by firing everyone who's just sitting around working crossword puzzles."

Martinez responded that Thomas is "a car dealer who appears to have been in too many demolition derbies." Alarmed by the furor, Martinez plans to seek a public vote on the service-tax issue.