The whole “army and Charadim” is a red herring.
The chilonim don’t want Charadim in the army, but they do want to stop paying for their services, and are afraid that they will take over the country through the vote (and large families). The Charadim don’t want to be in the army, but do want the services and do plan on taking over the country and making it a “Religious state”. Short of that, they want to be left alone, as they are “conscientious objectors” to the state in general.
The simple (and sometimes suggested) solution is to have anyone at 18 either sign up for Army/Sherut, or agree to drop their citizenship voluntarily (which would make them stateless, but would not go against international law, since it is voluntary), They would be allowed to remain in the country legally (similar to what might have happened in an Arab state), but lose the vote and the right to services (such as health care, etc.). It would give the Charaidim everything that they claim that they want, but would never be accepted by them.
Al Shelosha Devarim HaOlam Omed: KESEF MAMMON GELT!!!