To the insane and mentally unstable or those they have terrorized or brainwashed, you can justify almost anything. I will take up this part of your question:
How would you explain Exodus to these extremists so as to discourage this kind of justification?
First, Moses, Aaron, and the people of Israel DID NOTHING except believe (and paint their doorposts with blood). They did not cause frogs to leave the river or the sky to turn dark at midday. God did those things.
“It is mine to avenge; I will repay,” says the Lord. (Romans 12:19)
Thus I would say, believe all that you want that certain forceful practices against unbelievers are justified and call on God to do them - but leave it to Him. It is not your place to do those things.
It is true that the Egyptian priests and magicians duplicated the first few signs. Given that, the initial assumption of the Egyptian people was that Moses was personally performing these miracles, hence was responsible for terroristic acts. But as the plagues worsened, even the religious establishment in Egypt was forced to conclude that it was not the work of a man, but a god.
Second, this was not a war (not until Pharaoh sent his army to march against them at the Red Sea), so talk of "just wars" is not relevant. Each plague either had as its agent a creature or force of nature that was worshiped as an idol by the people of Egypt (like frogs), or caused the death of something they worshiped (like cattle). Each plague was an example of God saying, "This is not a god, this cannot save you, so do not worship it." All the people of Egypt worshiped these idols, except the Hebrews, and I imagine many of them did as well (as the Golden Calf episode would attext), and were forced to make a choice. Thus all the people of Egypt were guilty of idol worship and were deserving of punishment. God in his mercy slowly increased the severity of the plagues, giving them a chance to abandon their ways. It was not a war - it was a judicial action by God, the judge, against individuals, and every Egyptian was individually responsible.
Third, The Hebrew people's action was to insist on religious liberty - the right to go into the desert and worship their God. Theirs was a legitimate act of civil disobedience against a genocidal empire that had tried to kill all their male children. When a state commits genocide, the people who are being killed or enslaved have the right to self defense, and the genocidal actor loses all legal right to govern them. Thus the actions by Egypt to suppress them are not legal, because they constitute a continuation of the genocide.
Terrorism: The unlawful use of violence and intimidation, especially against civilians, in the pursuit of political aims.
It was Egypt that had been carrying out terroristic actions against the Hebrew civilian population in the pursuit of political aims, not the other way around.
Fourth. One cause of the judgment was ingratitude. You might say, but how were the Egyptian people to know that they were worshiping idols? They were just following their leaders. The telling detail was that years before, God used Joseph to save all Egypt from a famine, and the people chose to forget that deliverance and not continue to show gratitude to the one who saved them or the people who kept alive the memory of that God.
God is one to show leniency in proportion to ignorance. The people of Egypt were not ignorant, so they were not innocent. They were guilty. When confronting people, you must likewise show restraint. How much has the witness of God's truth come to a people or a person? That must temper your approach when speaking up for the truth.