I like your topic a lot, but I haven't seen any association between the concept of "objective" aesthetics and an anti-modern bias. On the contrary, I usually associate the idea of objectivity in music with musical modernism.
Stravinsky's idea of music as essentially a structure in time formed one of the big pillars of his neoclassical period (1920s - 50s). The word 'objective' was even thrown around by him and others like Ernest Ansermet in describing his music.
The same ethos coexisted with or extended into (?) the practice of integral serialism in the mid-twentieth century. Composers carved music up into its component dimensions (dynamics, pitch, register, rhythm, timbre, etc.), looked at what elements were available in each dimension (forte, mezzoforte; C, C-sharp, D; etc) then organized the content of each dimension essentially separately, each according to a well-defined structural principle, like an ordering or combinatorial scheme. The terminology that went with serialism took on a sort of mathematical ring. Boulez had a technique that he called 'multiplication.' Babbitt who had a background in math added jargon like 'derivation,' 'set,' 'aggregate,' 'array' and so on.
Early minimalism shared with serialism a similarly distinctive emphasis on objectivity. Lamonte Young's unique and strictly math-based tuning in The Well-Tuned Piano, Steve Reich's goal to make the musical 'process' as straight forward as possible are some examples. Reich's Pendulum Music allows the laws of physics to dictate the form or musical process by swinging multiple microphones suspended by cords and listening to the resulting phase shifts.
Now there's computer-aided algorithmic composition. Computers are the kings of objectivity. Blah, blah, blah: you could go on and on enumerating the various manifestations of objectivity-ophilia in twentieth-century music.
An 'objective' view of music is not at all unique to the twentieth century, but it introduced to the twentieth century a major shift in tone from the late nineteenth and early twentieth centuries, where musical structure was generally viewed as the vehicle of affect.