I suppose one of the functions of education is to transmit the accumulations of a culture/civilization, but it's not that simple. If you can't do Persian arithmetic, or ancient Greek trig, you are in trouble in life. Western civilization has always been open to interesting new ideas. Case in point: Christmas tree.
In "modern times", ie, say, that includes other world cultures too. Perhaps "modern times" in the West sort of began with the Roman Empire.
Modern Western civilization has borrowed much from the entire world, and made something wonderful out of it all. Sometimes I wonder that Christianity could only have emerged from the Middle East with its hodge-podge of cultural and religious history. Mostly Jewish of course, but far more than that.
I think it's great to learn about other civilizations and cultures, but I think Western people need to know their own first. Like a language. Or, including the language.
My feeling is that Western civ contains astonishing wisdom and thought - more than anybody's brain can contain. I include Jacques Barzun and Einstein in that. Legal theory, math, literary adventures, philosophy, religion, etc. You can read about Canadian aborigine medicine on your own time but it's not so easy to get a grip on Biochem.
If the kiddies can't get it through their parents, they have to learn it all from schools. The Greatness the Professors Denied