Eve is largely blamed for the Fall of Man in the Old Testament.
In the New Testament, Jesus' apostles are all males. Jesus himself is male. The OT God is very masculine. So apparently if God has a gender, it is definitely male, according to Judeo-Christianity. Not only is woman not God, she is clearly problematic (Eve), as viewed through biblical doctrine. An even more profoundly clear statement on that is in the Gospel of Thomas, where Jesus supposedly says that "every woman who becomes male will enter the kingdom of heaven". So yes, it could easily be argued that this is all a foundation for sexism to a profound degree.
Eastern teachings like Taoism (with its Yin-Yang balance) or Buddhism which doesn't even touch the issue of supreme deity, let alone gender of such a deity, have less of this going on (although this issue can be found in Buddhism as well; apparently the Buddha denied women entry into his religious community at first, and when he finally agreed, said it would bring about the end of his religion faster). Hinduism does posit a supreme Being, "Brahman", which is often viewed as masculine, but feminine expressions of this deity abound within its polytheism (Kali, Shakti, Durga, Tara, etc.). In fact, India is the only major culture where the feminine forms of the divine are still strongly prevalent.
Spiritual teachings like Tantra delve deeply into male/female differences, and I think that some of these teachings exist in esoteric forms in doctrines like the Bible, but are not usually interpreted that way. All that seems plainly obvious is that Eve is cursed (Gensis 3:16), as the prototype woman who is to be "ruled over" by her man.
Some Gnostic teachings view this all in reverse, incidentally, putting forth the idea that the Serpent is the teacher, bringing free will to humanity, and that Eve has the greater courage to explore this free will. Jehovah is simply the custodian, and as such shows all the personality traits of the controller, both good and bad. Free will in that sense is necessary in order to establish separation, a process in some schools of psychology called "differentiation". Without this phase in development, maturity is not possible. So the entire process of Mankind's spiritual redemption and maturation could not have occured without Eve's rebellion. Eastern teaching also refer to this process in cycles of reincarnation wherein the soul cannot properly evolve without first exploring the lures of Maya and Shakti, the goddesses of the manifest universe.