Answer

I don’t know what the recent events are.
I don’t think the IDF is trying to restrict the religious. I do think it is giving in to others, some of whom have an excessive liberal agenda, and some of whom really are trying to restrict the religious.
I don’t have a position regarding a mixed battalion, because I don’t know exactly how it works.
I do not encourage women’s service in the army, although I don’t think there is any real prohibition involved. In my opinion, it is possible to contribute no less, and perhaps more, through national service, and there is no real reason for women to enlist. My impression is that the army also does not truly need that manpower. The main purpose of drafting women is equality, not military necessity.
I don’t think there is a way to fix the situation. Each person has to weigh his own considerations, and if someone thinks he is not prepared to serve in a mixed battalion, he should refuse to do so. If a rabbi thinks it is forbidden, then he should forbid it to his students. There is no need at all to be impressed by the automatic scoldings of the sanctimonious. If there are enough such people, the army will have to consider whether the gain is worth the damage or not. This is a matter of pressure against pressure, and contrary to its public image, the Religious Zionist public usually does not exert pressure on the army, but rather gives in across the board on every front, and therefore always loses and is always discriminated against despite its contribution. These soldiers are required to listen to women singing and to serve in mixed battalions, something that no one would even think of demanding from Haredi soldiers. The same is true regarding kashrut and other matters. Someone who is taken for granted is naturally not taken into account. Someone who is never willing to break the rules of the game will never achieve anything.