Nearly 360,000 registered voters in California could be shut out from the state's June primary after accidentally registering with the wrong political party.

A Los Angeles Times report found that half a million Californians unwittingly belong to the ultraconservative American Independent Party — but nearly three in four thought they were registering themselves as "independent," or not belonging to any political party.

California's top-two primary system allows people to vote for any candidate, regardless of party, except in presidential primaries.

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Republicans have a closed primary this year. Democrats will allow voters registered as having "no party preference" — California's official term for an unaffiliated, independent voter — to cast ballots in their primary. But voters who are registered with the American Independent Party can only vote for presidential candidates on the AIP ballot.

Members of the AIP make up 3 percent of the state's 17.2 million registered voters. The party's platform opposes abortion rights and same-sex marriage and calls for building a fence along the entire United States border.

Many of those interviewed by the L.A. Times were shocked to learn they belonged to a party supporting such ultraconservative positions.

Those include some of well-known celebrities such as Kaley Cuoco from "The Big Bang Theory," actress Emma Stone and boxing legend Sugar Ray Leonard, all three of whom said their registration with the party was a mistake they planned to fix.

Those who have mistakenly registered with the AIP still have time to change their affiliation before the state's June 7 primary. The deadline is May 23.