Was conscription morally justified during World War I?

The answer to your very interesting question will depend upon your perspective regarding war. First, you will have to decide whether the war was justified.
Was World War I fought to defend the innocent, assist invaded allied nations, or stop human rights violations? This would be consistent with what we call the just war theory. The Allied Powers of World War I (mainly consisting of Britain, France, Russia, Italy, and the United States) would have argued that the war was a just war. Meanwhile, the Central Powers (consisting of Germany, Bulgaria, the Ottoman empire, and the Austrian-Hungarian empire) would have made a similar argument.
Ostensibly, the immediate cause for World War I was the assassination of Archduke Ferdinand, the heir to the Austro-Hungarian empire. However, the real reason for the war was that certain major powers of Europe were angling for dominance of the continent. In the end, alliances solidified, leading the British, French, and Russians to form the Triple Entente, while Italy, Germany, and Austria-Hungary formed the Triple Alliance. 
Germany nursed hegemonic ambitions, and many historians believe that the country was the main aggressor during World War I.
To get back to your question, we must decide whether Germany's ambitions were valid and whether the Allied powers were right to defend their countries from attack. We must remember that both the Triple Entente and Triple Alliance members conscripted soldiers to fight during the war. The Bulgarians and Italians conscripted 55% of males from 18-50 to fight, Austria-Hungary conscripted 78%, and France and Germany conscripted 81%.
At the same time, Britain and the United States also instituted a draft during the war. In addition to those drafted, there were a few million men who volunteered to fight for both armies. If the just war theory holds, then war was justified on the side of the Allied powers. 
As for conscription, we must decide whether individual rights supersede the responsibility to defend one's country in the event of an attack. This is the crux of the issue.
http://www.bbc.co.uk/ethics/war/just/cause_1.shtml

https://www.bl.uk/world-war-one/articles/recruitment-conscripts-and-volunteers