Drafting Women to the Army

From what I recall, and pardon me if I do not remember it entirely accurately as it was a long time ago, as I was approaching the age of 18 years, I was required to register for the US armed forces draft. Even though there is no forced or automatic conscription and it is all voluntary, we had to register, in case one day the USA would decide to go back to a compulsory draft.
I do not think I even knew this but it seems that requirement to register was only for male citizens, not females.
It seems the US government is considering a bill that would require women to register for the draft as well. The bill has been in the works for a while now and it continues to move forward bit by bit to eventually be passed into law. The House Armed Services Committee just voted in favor.
To stress, this law, should it pass, does not mean women will be drafted into the armed forces, but they will have to register in case one day there will be a compulsory draft.
The move is based on the current law requiring registration of men to be discriminatory against women.
Haredi newspapers in Israel (Hamevaser, Hamodia) are reporting that Agudath Israel of America is working to put a stop to this before it becomes law and has requested the US government reconsider before it becomes law.
Obviously conservatives and religious groups will be opposed to this law. I don't see the US government right now backing down from this, as equality and non-discrimination is one of today's highest values. Perhaps they will agree to include some sort of religious exemption. Even though it is only an issue for a theoretical day in the future, Agudath Israel can't let it sit and wait until that day should actually happen. In Israel women can get a religious exemption almost automatically
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