My mistake. Arrow Cross was Hungarian. Austria-Hungary (Catholic) was anti Serb (Orthodox) in the WW1 era and before
There were several million Orthodox Christians living in Austria-Hungary, and plenty of them served in the armed forces.
As I explained, this was not a religious matter. Austria-Hungary also went to war alongside Lutheran Germany against Catholic Italy and Catholic France and allied itself with Orthodox Russia against Lutheran Germany.
The issue is that Serbia stood between Austria-Hungary and full access to the Mediterranean. Look at the map of Europe: Austria-Hungary's western rival - Catholic Italy - controlled the northern and western Adriatic. Austria-Hungary - through Slovenia and Croatia - had access to the eastern Adriatic, but Serbia - through its ally Montenegro - controlled one half of the Strait of Otranto and Italy the other half.
The Strait controls access to the Mediterranean.
In order to become a reputable naval power with unfettered access to the Mediterranean, Austria-Hungary needed Montenegro and the path to Montenegro was blocked by Serbia, Montenegro's partner.
Serbia was the only barrier between Austria-Hungary and world-class naval power.
Franz Joseph did not care whether the people blocking his access to the Mediterranean were Orthodox or whether they were his own grandmother.