I don't believe it to be a highly religious holiday, though it has religious beginnings, but you're not quite right about "Paddy". https://www.krqe.com/news/weird/st-pattys-or-st-paddys-day/

The correct way to abbreviate St Patrick's Day is St Paddy's Day. This comes from the Irish spelling of Patrick which is spelt Pádraig and nicknamed Paddy. People in Ireland and Northern Ireland do not use the abbreviation 'Patty,' this version is mostly used in America