After the Revolutionary War, the states insisted on the constitutional right to defend themselves in case the fledgling U.S. government became tyrannical like the British Crown. The states demanded the right to keep an armed "militia" a form of insurance.
Article 1, Section 9. of the U. S. Constitution:
No state shall, without the consent of Congress, lay any duty of tonnage, keep troops, or ships of war in time of peace, enter into any agreement or compact with another state, or with a foreign power, or engage in war, unless actually invaded, or in such imminent danger as will not admit of delay.
So by the ACLU's interpretation, the signatories to the Constitution signed onto the Second Amendment and immediately declared Section 9 null and void since a tyrannical federal government could simply deny to the states their consent to keep troops. All the signatories who wrote that they simply wanted to have the Bill of Rights declare some rights not stated in the Constitution are liers. On one hand they signed a document stating that the states cannot have troops without the consent of Congress and yet they wanted the states to have the ability to resist the federal government (I guess without troops, or did they expect a tyrannical federal government to give consent to the states to keep troops?).
If you take a contradictory view and see the Second Amendment as giving the people a way to resist a tyrannical government, then there is no conflict. The states are still prohibited from maintaining National Guard troops without the consent of Congress and the people can still form militias to resist a federal government that might withhold that very consent. It is impossible to reconcile the ACLU's position.
Irreconcilable indeed, except that they are a Communist front organization intent upon disarming Americans before they dismember us.
For which, they will fail (and their failure will be quite painful).