Final answer:
There is no specific term for 20th-century composers labeled 'sell-outs' by modernists; however, the divide was between modernist composers like Schoenberg and those who extended Romantic traditions, like Mahler and Strauss, while remaining accessible to a wider audience.
Step-by-step explanation:
20th-century composers who were accused of being "sell-outs" to the public's musical tastes by modernist composers do not have a specific term that universally categorizes them. During the early 20th century, a musical divide had formed, where some composers strove to break away from traditional musical forms and create what is known now as modernist music. This movement included artists like Arnold Schoenberg, who experimented with atonality and the twelve-tone technique, which defied traditional scales and harmony that Western audiences were accustomed to.
On the other hand, composers such as Gustav Mahler and Richard Strauss pushed the boundaries of the Romantic era's musical language but remained more accessible to the general public. They were seen as continuing the Romantic tradition of emotive, lush orchestral music and were sometimes criticized by more radical modernist composers for not embracing the avant-garde approaches completely.
The term sell-out can carry a derogatory connotation, implying that these composers were compromising their artistic integrity for public approval. However, many of these composers were simply evolving within the musical language of their times, engaging with the traditions of their own countries (nationalistic music), or taking Romantic techniques to their limits without necessarily abandoning the desires of the listening audience.