Of course you have a responsibility towards the society and the people who raised and support you.

That just doesn't involve excluding others from that society. They deserve, just as much as you, to participate (and improve!) in your society as you do.

My country only exists because people came from many other societies and brought the best parts of those societies together to create my country and its culture. I want that for everyone, if they want it for themselves.

I doubt your country was the result of a bunch of people from a bunch of different countries coming together to create a new nation. It was almost certainly a group of like minded people who all came from the same place creating an offshoot that is influenced by the original.

Especially given that the ability for global communication is newer than most existing countries.

I’ll be sure to tell all American history books that Alexander Hamilton and Lafayette (two off the top of my head because I listened to Hamilton recently, there absolutely were many many more) were actually from England and not the Caribbean and France respectively.