The New York Times August 28, 1990, Tuesday, Late Edition - Final By RICHARD D. LYONS SINEAD O'CONNOR, the 23-year-old Irish rock star who has a history of throwing tantrums and getting her way, was singing a different tune yesterday about her concert in New Jersey on Friday. Ten minutes before the start of the show at the Garden State Arts Center in Holmdel, Ms. O'Connor threatened to walk out if the national anthem was played, a demand that was complied with by the New Jersey Highway Authority, which owns the building. The singer, who wears her hair at almost peach-fuzz length, was paid $75,000 for the two-hour concert, attended by 9,300 fans. On Monday USA Today quoted Ms. O'Connor as saying, ''I don't want to go onstage after the anthem of a country that's arresting people and harassing people for expressing themselves onstage.'' Yesterday she tempered her words by issuing a statement through her publicist, Elaine Schock. It said: ''This was not meant as a snub of Americans. There is a disturbing trend toward censorship of music and art in this country, and people should be alarmed over that far more than my actions of last Friday night.'' Some critics of her action are calling for a boycott of her performance tomorrow at the Saratoga Performing Arts Center in Saratoga Springs, N.Y.