Irish don't follow an ideology that thinks Sharia superior to all other Western Cultures or Democratic ideology.
No they don't. Most Irish people don't even think Roman Catholicism is superior to all other cultures. Nor do most Muslims think Islam is superior.
But there were Irish extremists (many of whom were not devout Catholics, but who wished to defend Irish Catholics from oppression) who were prepared to use terrorism to get their way.
And many Muslims today feel the same.
The solution to Irish Nationalist terrorism didn't involve more oppression of Irishmen. Why do you imagine that the solution to Islamic terrorism involves more oppression of Muslims?