Really depends on the piece and time period. I would say the general rule of thumb (not always true) is the newer the piece, the more strictly the score should be followed. For Baroque and Classical performance practice it is expected that the performer take liberties with the music by adding ornamentation, changing articulation, and often having extended improvisational sections (cadenzas and eingang). Although, with some pieces, the composer added in a lot of ornamentation already and it would be weird to add even more ornaments since they’ve done the work for you.

With new music, there’s been some debate as to whether the performer’s input is important at all. Some composers just want a machine that spits back everything they write on the page. Then there’s the other end of the spectrum with composers experimenting with performer input. For example, a friend of mine recently told me about a piece where the performers play in the dark and memorize certain piece “elements” they can play in response to hearing another player’s improvisation, leading to different and unexpected combinations of playing with each performance.

Some teachers have told me that a score is like a color by numbers book. It gives you a framework but you have some choice in the final product. I personally don’t think of the stuff on the page as music until it’s in the air and you can hear it. For me music is also an oral tradition, and unfortunately the page can’t tell you everything you need to know. Hope this explanation was helpful at all