In this quote "at stake" is not being used literally to mean at risk of being lost or destroyed, but figuratively to refer to a change in the popularity of a certain point of view. It means the thing is an important subject for consideration pending some kind of outcome which could be positive or negative.

Trends and viewpoints can rise and fall in popularity over time, and when a point of view is being challenged, it's "at stake" in the sense that the correctness or reliability of it may be called into question. People who have a vested interest in a specific point of view may see something that brings a point of view into question may see it as being put at risk in the same way that money could be at risk of being lost.

In this case there's a conflict between Modernism and Romanticism in 20th century music. Reading further you find this... "Scholarly objectivity with respect to history became a Modernist conceit."

In this quote "at stake" is not being used literally to mean at risk of being lost or destroyed, but figuratively to refer to a change in the popularity of a certain point of view. It means the thing is an important subject for consideration pending some kind of outcome which could be positive or negative.

Trends and viewpoints can rise and fall in popularity over time, and when a point of view is being challenged, it's "at stake" in the sense that the correctness or reliability of it may be called into question. People who have a vested interest in a specific point of view may see something that brings it into question as putting it at risk in the same way that money could be at risk of being lost.

In this case there's a conflict between Modernism and Romanticism in 20th century music. Reading further you find this... "Scholarly objectivity with respect to history became a Modernist conceit."