Hi Januka,
I am running GMT6.x on an old MacPro from ~2012 that uses 10.13.x High Sierra (and is not upgradable anymore). The way forward is to compile everything from source which should not be too much of a drama apart from taking more time. gdal has always been a bit of a pain but for the old system William Kygnesbury’s frameworks still work so that goes long way saving you the hassle of GDAL-dependencies (if you need functionality > GDAL 3.2, then you will need to compile this from source, unfortunately, as William’s frameworks only go up to GDAL v 3.2).
So what you’d need to do is to get the dependencies and effectively follow the steps detailed in the BUILDING.md document. Other than building things from source I wouldn’t have a suggestion. Possibly downgrading the version of homebrew, but again, that might not work and in the end turn out to be more of a time sink compared to building all from source.
Good luck,
Christian