I look for material in which the sexist ideology is related to religiosity and political orientation. I understand that atheist and left-wing people tend to maintain a more egalitarian ideology. I would appreciate your help. Thank you.
Often but not always, traditionalist religious beliefs are tied to patriarchy and therefore sexism. In the United States, many evangelical Christians came to adopt right-wing politics in the late 1970s when the Republican party strategically added opposition to abortion to its platform. Prior to that time, many American evangelicals were involved in advancing the cause of social justice, promoting racial equality in the 1950s and 1960s and working for abolitionism in the 1820s through 1860s.
Your question seems to predetermine the answer. You need t consider the question in neutral terms then arrive at an answer based on the evidence. most likely you'll find a correlation but it it best to remain objective until you do. You might look at
Forman-Rabinovici, Aliza & Udi Sommer “An Impediment to Gender Equality?: Religion’s Influence on Development and Reproductive Policy” World Development, 105, 2018, 48-58.
Htun, Mala & A. Laurel Weldon “Religious Power, the State, Women’s Rights, and Family Law” Politics & Gender, 11 (3), 2015 451-477.
Sweeney, Shawna A. “The Sacred and the Secular: Separation of Church (Mosque) and State & Implications for Women’s Rights” International Journal of Gender and Women’s Studies, 2 (1), 2014, 1-35.