Agreed. The Easter Rising, and the cause of Irish nationalism generally, weren't anywhere near as linked to Catholicism as this article makes out. It's much more correct to see it as a class struggle or a revolution against a colonial power, depending on your view (the ruling class were closely linked to Britain).
Prominent 1916-era nationalists like Childers and Markievicz were Protestants. Connolly was a hardcore socialist who would have embraced Marxist atheism. The Church didn't generally support the Rising, partly because it feared socialism. The Proclamation of the Irish Republic doesn't mention the Church, or even, remarkably for the era, God. Most importantly, perhaps, the Penal laws suppressing the practice of Catholicism were just a memory at that stage. Irish people were oppressed because they were Irish, not because they were Catholic.
I don't want to completely discount the link between Catholic and Irish identity - fostered by Pearse and then de Valera among others. But to emphasize it here smacks of an understanding of Ireland that comes mainly from late-20th-century international news and conflict in the North 'between Catholics and Protestants'.
Edit: I'm less familiar with the Russian revolutions, but my layman's understanding is that the class struggle was more important there too than imposing atheism. In Russia, the Church was part of the dominant power structure that had to be deposed: in Ireland it wasn't. It's not so hard then to align the movements.