Indeed - Cromwell wasn't an aberration, he was the start of the occupation of Ireland with all the usual brutality of colonialism, and the Orange Order will happily bring him out as a "stick" in the other direction.
The "English" running Ireland pre-Cromwell were predominantly Anglo-Irish lords, and were mostly Catholic.
Post-Cromwell, the brutality got much worse, and the Catholic vs Protestant dimension caused extremely repressive laws for Irish catholics: https://en.wikipedia.org/wiki/Penal_Laws