Does Israel have a draft? If so are both men and women required to register?
In Israel men and women are obligated in mandatory military service at age 18.
IINM men is 2.5 years (used to be 3 years) and women is 2 years (maybe shorter).
Women can get an exemption if they declare they are religiously observant.
IINM there's also an option to do civil service instead.
Yeshiva students have been eligible for a deferment since the early days of the state, as long as they certify that their sole occupation is studying torah. There have been various tinkerings with this throughout the years, with limits on ages, time, etc. But essentially it was previously an accepted procedure, and then later on the supreme court forced the government to enact a law. Ever since then it has been a contentious issue. First a law was enacted, then it was struck down by the supreme court, and ever since there have been various political solutions, fights etc. on how to resolve the issue.
While Israel probably no-longer NEEDS a mandatory draft, it is seen as a melting pot and entry into Israeli civil society.