I have also found that SVGs generated by S&S editor, as well as Gregobase, do not play well with Adobe Illustrator.
And in any case, Photoshop and Indesign, while they are able to open /some/ SVGs, should best be left out in favor of Illustrator - a vector object can then simply be copied and pasted from Illustrator to Photoshop and Indesign.
I think there is no fix to this problem. However, there are several workarounds :
- the easy but limited way : switch online "editors" (S&S & co. should more aptly be called "previewers" because GABC is really meant to be compiled and not rendered on the fly) in favor of Chant Tools : https://bbloomf.github.io/jgabc/transcriber.html
(click "show integrated GABC" and paste your code) ; then "Download SVG". Chant tools is not as feature-rich as S&S (they are both works of the same person, all hail Benjamin Bloomfield) so this will work for basic stuff but not for the rarer note shapes and other complex GABC features.
- the easy but ugly way : export PNGs from S&S / Gregobase / Chant Tools, and work with PNGs in the Adobe Suite.