The newly reorganized Senate Labor and Human Resources Committee yesterday held its first hearing on sex descrimination in the work place, and the occasion appeared to be a cautious mutual courtship between the conservative Republican committee chairman and some of the most outspoken advocates of equal rights and equal pay for women.

For their part, leaders of some of the most visible and active women's rights organizations appeared willing to give Chairman Orrin Hatch (R-Utah) the benefit of the doubt while making it clear that they oppose his views on the Equal Rights Amendment and affirmative action.

For his part, Hatch frequently reiterated his concern for women's rights, attempting to set aside the controversial issue of ERA and continuing to assert that affirmative action had led to abuse and quotas.

Hatch emphasized enforcing existing laws aimed at correcting discrimination against women and brushed aside the ERA as an issue to be determined by the states. But the issue kept coming up anyway.

"It's doubtful that we will see economic equality without the ERA," said Karen Nussbaum of Working Women, a national association of office workers. Other speakers also made it clear that the constitutional amendment, often viewed as a now-hopeless case, is a top priority.

Witnesses yesterday recited the statistics that define the inequal status of women in the work place. National Organization for Women President Eleanor Smeal noted that men are paid more than women at every age level and that even in professions which they dominate, such as clerical work, women are paid less.

Representatives of women's rights groups generally were positive about the committee after the meeting. "We have a responsibility to millions of women to find where we can agree and can work with the leadership," said Iris Mitgang, who heads the bipartisan National Women's Political Caucus. Mitgang noted that Sen. Paula Hawkins (R-Fla.), generally not considered a feminist, appeared responsive on the issue of displaced homemakers and child care at the work place.

Sen. Claiborne Pell (R-R.I.) asked one panel of five women if they would support draft registration for women. Four of them -- Nussbaum, Shirley Sandage of the Displace Homemakers Network and Jane Fleming and Avril J. Madison of Wider Opportunities for Women -- said they would support registering women only after the ERA is adopted.

The controversial amendment -- opposed by President Reagan, the Republic platform and many conservatives -- is three states short of the 38 needed.