IF JEws don't blame Eve for being the first to sin, then how come its women who are afflicted with the pains of child birth and it is says taht the woman's yearning will be for her husband and he will be the master/lord what ever term the Hebrew Torah uses over her. I have heard many Chrsitians who have used your interpretation and many Jews who believe that it was Eve who was deceived and then misled the husband. As far as I can see it, our views are the same, depending on whether you come from the pro-woman or pro- man way of thought. All the beliefs are interpreted by JEwish or Christians scholars in simliar ways. Some lean towards the man being at fault, some say woman, some say both. I don't think you have any means to go around saying Christians blame Eve for sin and therefore treat women bad. Women were treated very bad in their societies around the world and were treated less than human and JEsus gave them a position of honor and respect and allowed them to be apart of his ministry and enter their synagogues (or what is now called churches), where they preached and congregated. He forced peopel to wake up and look at women as mothers, sisters and daughters. He help gave an active role in the church and got them involved in spreading the Word and helping others. As far as I know at this time, women in most of the world, except in Persia and few other places, where not allowed to have any interaction with men or be active members of the ministry or society. Paul wrote there is now no Jew nor Gentile, nor slave or free , nor man or woman to counter, meaning everyone was welcomed to be apart of the religion and treated with respect.
Islam is taken from arabic paganism where mutilating your wives and collecting groups of women to be your so-called wives/prostitute store was the norm. Arabs have always been treacherous to their women. Islam did liberate women , as they do claim, in the context of arab pagan society. Since they learned some Judaic-Christian values they now realized that they must now have a reason for cutting off their wives haed. IN olden times, Arabs would just behead their wives and leave the min desert; they were not even a human or any life form worth more than a donkey.
Every religion has woman beaters. Don't use the example of the one wife beater as reflecting Christianity and I won't use any example of black lesbian rabbi as representing Judaism.