How did Southern conservatives try to limit women and African Americans from enjoying the full benefits of the New Deal?

Franklin D. Roosevelt's (FDR) New Deal was a program designed to dig America out of the Great Depression by creating public work projects, financial reforms, and business regulations. Some of the programs created were the Civilian Conservation Corps (CCC), the Civil Works Administration (CWA), the Farm Security Administration (FSA), and the Social Security Administration (SSA), to name just a few. These programs were designed to bring economic relief to the nation by providing jobs for the unemployed and support for struggling farmers. Because FDR was a progressive "liberal" Democrat, some of his ideas were met with resistance by Republicans and conservative Southern Democrats.
In order to guarantee that his New Deal was a legislative success, FDR often had to court Southern conservative Democrats to ensure that the racial and gender inequalities of the traditional South remained intact throughout his programs. In this way, conservative Southern Democrats had a hand in limiting how much African Americans and women could benefit from the New Deal.
By 1936, about 75 percent of black voters supported the Democrats and, by extension, FDR. Although FDR's civil rights record was unimpressive, Southern African Americans had been slighted by Republican initiatives and were excited by the prospects of the New Deal. Unfortunately, FDR's administration consistently caved to pressures from Southern conservatives in the party to limit how much black people could benefit from New Deal programs.
For example, the National Recovery Administration (NRA) offered white people job opportunities first, and African Americans last. The Federal Housing Administration (FHA), refused to grant mortgages to black people who tried to buy in white neighborhoods, and the CCC remained segregated. The SSA also excluded jobs or job categories that were largely populated by black people, meaning that many African American were banned from benefiting from social security. All of these limitations were designed to safeguard white supremacy in the South in order to ensure support for the New Deal by Southern conservatives in congress.
Furthermore, the AAA allowed landlords of the South to make more money when land remained unfilled (as opposed to if there were tenants renting and working the plots). Because 40% of all African Americans in the South were tenant and sharecroppers, white landlords kicked them off their farmland, leaving over 100,000 black Southerners unemployed.
FDR also refused to support an anti-lynching bill or a bill to abolish the poll tax. Poll taxes were taxes that had to be paid before one could vote. Since black people remained socioeconomically disadvantaged, many could not pay the tax and thus could not vote, helping white voters to suppress black-supported candidates. FDR was worried that, if he supported these pieces of legislation, conservatives would turn their backs on his programs.
Likewise, FDR sought to maintain the South's male-dominated social hierarchy. His public works projects were mostly subsidies of large construction undertakings (designed for men), while women's jobs under the provisions were much less visible (domestic work, sewing projects, food service, etc.).
Even though women had been hit hard by the recession, FDR made little effort to create more work for them, particularly married women. Many teachers and daycare workers (mostly women) had lost their jobs when schools closed. However, the ethos of the time (particularly in the South) was that if a woman's husband was working, she didn't have to. It was an accepted norm that a husband be the "breadwinner."
However, this failed to take into account the many female-headed families in America, and eventually the WPA was formed. This program hired single women, widows, or women with disabilities to unskilled jobs sewing clothing and bedding for orphanages and hospitals. Women were also hired to the WPA's school lunch program. Unsurprisingly, women's jobs under the WPA were lower paying than the male-centered jobs created under the New Deal.
http://www.digitalhistory.uh.edu/disp_textbook.cfm?smtID=2&psid=3447

https://womensenews.org/2009/02/new-deal-slighted-women-in-recovery-plans/

https://www.history.com/topics/great-depression/new-deal