Thousands of jobs and job training positions for hard-core unemployed have become embroiled in a church-state conflict over federal funding for workers at church-run schools.

The controversy revolves around use of Comprehensive Employment and Training Act (CETA) funds for on-the-job training such as library and teachers' aides and custodial employes at Roman Catholic parochial schools.

The CETA program allows subcontracting agencies to hire "economically disadvantaged and long-term unemployed" for jobs aimed at preparing them for non-subsidized work.

In October, the Wisconsin Civil Liberties Union brought suit against the Department of Labor, which administers CETA, to block the CETA program from church-sponsored elementary and secondary schools in Wisconsin, particularly in the Milwaukee archidiocese. The WCLU suit charged that church schools' involvement with CETA violated First Amendment guarantees of seperation of church and state.

According to officials of the United States Catholic Conference here, attorneys from the Labor Department and the Department of Justice agreed in November to a plan under which all CETA workers would be withdrawn from the Milwaukee church schools. The agreement with the WCLU reportedly also called the new nationwide directives from Labor that would exclude all church schools from future CETA funding.

A Labor Department spokesman dereported agreement because "the matter is in flux."

According to a Catholic Conference memo made public this week, General Secretary Bishop Thomas C. Kelly protested that projected elimination of the CETA jobs in December to Labor Secretary Ray Marshall, Secretary of Health, Education and Welfare Joseph A. Califano Jr. and Associate Attorney General Michael Egan.

As a result, the memo relates, Labor and Justice Department attorneys "withdrew from the tentative agreement to a consent decree in the Wiconsin lawsuit" and the new directives were not issued.

The Justice Department's Office of Legal Counsel, however suggested in a Jan. 25 memo that CETA funding of jobs such as health aides and kitchen personnel would be allowable. But it said funding of other jobs, "including those involving teaching or counseling, maintenance or most clerical responsibilities is . . . precluded under recent decisions of the Supreme Court."

Neither the Department of Labor nor Catholic offices here could say how many jobs are involved.