Rep. Harold Washington (D-Ill.) ran into his second round of organized heckling in a racially charged mayoral campaign here as several dozen placard-carrying white residents of a northwest side Polish and Irish neighborhood taunted him today on his way in and out of a church social hall.

Washington, who is black, deflected the protesters by smiling, waving and blowing kisses. When they shouted "Ep-ton! Ep-ton!"--for Washington's Republican opponent, Bernard E. Epton--he tried unsuccessfully to address them.

Inside, at a gathering of Greek Americans who are supporting his campaign, he explained, "I wanted to ask them if I was their second choice."

Washington delayed his departure from the church hall for several minutes until police arrived. He pushed his way back through the jeering crowd without incident.

Protesters said their demonstration was a spontaneous one, but they were carrying printed Epton placards which they said had been distributed by the Republican and Democratic 36th Ward organizations--both of which are supporting Epton. A handwritten sign advised Washington to "go crawl in a hole somewhere."

Last weekend Washington and former vice-president Walter F. Mondale were kept from speaking in a northwest side church by more than 100 protesters.

The incident occurred on Washington's only foray today into a white neighborhood. He had spent most of Easter Sunday hopscotching to black churches, where he combined appeals for racial unity and black pride with cutting attacks on Epton.

"My past is known, my record is known," Washington told reporters outside the Carter CME Temple on the South Side, "but you don't know anything about my opponent. Where did he get his money? When did he get his money? How did he get his money?"

Washington has accused Epton of a conflict of interest for being a partner in a law firm that represented insurance companies while he served as ranking Republican on the state House Insurance Committee.

According to a report Saturday by the Illinois Public Action council, a coalition of citizens groups, the Epton firm received more than $1.3 million in fees from insurance clients from 1978 to 1982. The report charged that Epton was "enmeshed in conflicts of interest so pervasive that he . . . sold his House seat" to the insurance industry.

Epton, who did not campaign today because of the holiday, has denied any conflict and noted that as a legislator he championed bills protecting insurance buyers.

Washington, clearly seeking to neutralize the integrity issue that has cost his campaign dearly, stepped up his request that Epton release 10 years of tax returns and a full list of clients. The Republican has declined.

Because of that, Washington said today that he will not agree to a second debate with his opponent before the election April 12. "I'd salivate over the chance to debate ," he said. "But I'm not going to debate a man whose hands aren't as clean as mine."

Washington also repeated his call on Epton to make a full disclosure of his medical records. Late Saturday night Epton released a two-page medical history in which he revealed he was diagnosed as suffering from depression in 1975 when he spent two weeks in the psychiatric unit of a local hospital being tested for stomach ailments. The ailments were diagnosed as an ulcer.

Washington's past includes a conviction for failure to file tax returns and a disbarment for taking funds from legal clients without performing contracted services. Today he called those transgressions "minor flaws . . . for which I have paid my dues."

Race, the campaign's key underlying issue, was also very much evident today.

In his Easter sermon at Holy Name Cathedral, Cardinal Joseph Bernardin, head of the Chicago archdiocese's 2.4 million Roman Catholics, noted that "whether intended or not, racism has been a factor in the mayor's race, giving rise to some ugly whisperings and causing people to do and say things they would not normally do and say." Bernardin urged that people "rise above all this."