First of all the young Israelis are more secular then religious. Secondly the largest group within the settler movement are modern educated with a total respect for women. The ultra-religious are a small group who keep themselves insulated from most of Israeli society. It is this group that you see as having a problem with equal rights for women. As in all societies which have ultra religious movements...not just Israel.
Islamic State destroys part of Syria's Temple of Bel, monitoring group says (Reuters)
from the article: Spain recognizes Israel as Jewish homeland, for first time