Well, when Cromwell and the Puritans executed the king Charles I and got rid of the monarchy and so called "purified the Anglecan church", they also got rid of the Catholics. Then Cromwell took over N Ireland and declared it protestant. However, over time, people realised how stupid the Puritans and Cromwell were and reinstated the monarchy with Charles II as king. Then you got France and Louis XIV who revoked the Edict of Nantes and got rid of all the Protestants. Just another reason why religion should NEVER become part of the state.
However, after a while in England, James II I believe was a catholic king. When he had a son and baptised him catholic, parliament said no no there. They sent for William of Orange too come in and take over. William came in and kicked out James II without any bloodshed. That is why they call it the Glorious Revolution.
If the Orange Order is celebrating the fact that there was no bloodshed, then more power too them. However, this isn't the case. They are basically just rubbing it in that they are Protestant and the Protestants won in England. And parading through Catholic neighborhoods is just plain stupid. It is nothing but macho crap.