The Reagan Cabinet lost its only Democrat on May Day when Secretary of Education William J. Bennett, without fanfare or even announcement, walked into a neighborhood public library in Charlotte, N.C., and changed his voting registration to Republican.

Bennett has not been much of a Democrat following a little left-radicalism in college days. He has voted Democratic in only one presidential election, and has been pondering for over a decade whether to switch parties. What held him back was vestigial belief that the Democrats really are the party of the people. What finally moved him was his ancestral party's opposition to Nicaraguan contras.

His belated conversion to the GOP at age 42 merely formalizes Bennett's long-standing status. As a nominally Democratic neoconservative, Bennett has sounded more Reaganite than lifelong Republican colleagues in a mature administration taking on the party's traditional gray tint. But formal conversion permits a future in elective politics by the Cabinet's most charismatic figure.

Unlike such famous defectors as John B. Connally and Jeane Kirkpatrick, Bennett was never a Democratic luminary and not interested in partisan politics until recent years. His first presidential vote, at age 21, for Lyndon B. Johnson over Barry Goldwater, was his last for a Democrat. As a 29-year-old assistant to Boston University President John Silber, he began thinking about becoming a Republican while watching Democrats nominate George McGovern for president.

Then, what took so long? Unlike Kirkpatrick and Linda Chavez, Bennett was not advised by national Republican strategists (scarcely aware of his existence) to stay Democratic as a matter of 1984 campaign tactics. Rather, his own cultural bias delayed him.

''Remember the background,'' Bennett told us. ''I'm from Brooklyn, Irish Catholic, always thought of the Democrats as the party of the people and the Republicans as the country- clubbers. To leave the Democrats was like leaving the Catholic Church.'' Besides, close associates say, Bennett still did not feel entirely comfortable with Republicans, even after joining the Cabinet last year.

Nor did he fit the decorous model for Ronald Reagan's second term. Zealous support for the Reagan budget's attempted trimming of student loans as he took office led columnist David Broder to nominate him ''for the dubious award as the James Watt of the second Reagan Cabinet.'' That worried the White House.

So did the draft of Bennett's speech last August to the Knights of Columbus extolling the nation's Judeo-Christian tradition. An aide to chief of staff Donald T. Regan advised Bennett to go slow, but he gave the speech anyway. While most Cabinet colleagues stayed in the shadows, he attacked birth control clinics, bilingual education and the education establishment.

That made nominal Democrat Bennett an instant favorite on the Republican speaking circuit, just below the likes of George Bush, Kirkpatrick and Jack Kemp. At a party dinner in Michigan's 14th Congressional District, Bennett perceived that the GOP was turning into a heterogeneous, multi-ethnic party. He was fascinated that the Republican congressional candidate was Stanley Grot, who had immigrated from Poland in 1969.

One more shove was needed. It came in April while the secretary was in office watching over television as one House Democrat after another rose in opposition during the contra debate. Turning to an aide, Bennett noted that on May 1 he would be in Charlotte -- his wife's family home, where he was registered as a Democratic voter. That, he said, is the time to switch.

The switch is more than one private voter's decision. He has been talking politics with Republican old pro Lyn Nofziger, who considers him prime candidate material. Bennett also has huddled with New Rightist Paul Weyrich and expressed admiration for his Washington Post article on cultural conservatism. If orthodox Republicans are frightened by Weyrich, neoconservative Bennett finds his theories of cultural breakdown the key to the political future.

*Bennett broke the calm of a recent Cabinet meeting by warning that drastic action is needed to prevent the Reagan administration from presiding over a drug explosion. At a House hearing, he collided with Democratic Rep. Charles Rangel of New York by suggesting drug users be thrown out of school. The newest Republican is trying to set the party's agenda for the future.