There were two major beliefs that contributed to this sort of legislation.
First, there was the belief that women should be kept as much out of the workforce as possible. This was a remnant of the idea of “separate spheres” that had been in existence to some degree for decades. There was still a strong feeling (particularly among more traditional and conservative people) that women were best suited to working in the home.
Second, there was the idea that allowing women to work would take jobs away from the men who truly needed them. This was the idea that the jobs were zero-sum and that giving them to one group meant taking them away from others.
Thus, economic ideas about jobs and social ideas about the place of women combined to underlie the laws you mention.
New Deal work reforms largely benefitted the following industries: agriculture, finance, waterpower, and manufacturing. With the unique exception of World War II, at which time women were employed in munitions and other industries due to the absence of men, women did not work in these industries.
This is not to say that women did not benefit at all from the New Deal. The Federal Art Project was part of the Works Progress Administration (WPA). The project employed over 10,000 artists to work on a variety of projects from murals to sculpture to documentation. Many white women and people of color benefited from the program. Though these people profited from their unique talent, this opportunity is important; female artists are less likely than male artists to have the privilege to work on their art, especially during times of economic hardship. This program created more equal opportunity between the sexes in the arts.
However, as the previous educator mentioned, women who were not artistically inclined generally worked at home. Those who did not were employed as nurses, secretaries, or teachers—fields more often associated with women.