Disclaimer: I am not trolling, I am an autistic person who doesn’t understand so many social nuances. Also I am from New Hampshire (97% white), so I just don’t have any close African-American friends that I am willing to risk asking such a loaded question.
Others have given you solid answers on why the chicken and watermelon thing was really stupid so I'll try to answer from the Irish perspective on the second part of your question:
You can serve me corned beef and cabbage on St. Patrick's day as long as you're not being a dick about it. I'd probably consider it a nice effort actually if I happened to be abroad on the day.
My dad used to love corned beef, cabbage and potatoes with parsley sauce. It's a grand meal but not my thing.
If you were a unionist who served it to me in a leprechaun outfit I'd be inclined to tell you where to go though.
Edit: I hope this answers your question. It's a good question and the answer is nuanced so if I can offer you more perspective let me know, I'd be happy to help.
Years and years ago at a house party, some woman from Cork and a friend of mine from Belfast were joking and they said, “Because Ulster says”, and I had no idea what they were talking about.
The lad in the picture is Ian Paisley. He was a prominent unionist back in the day. (Unionist being someone in favour of maintaining the six counties in Northern Ireland being part of the UK)
From the wiki page:
Ulster Says No was the name and slogan of a unionist mass protest campaign against the provisions of the 1985 Anglo-Irish Agreement which gave the government of the Republic of Ireland an advisory role in the governance of Northern Ireland.