Sublime Text Does Not Let Me Save My Files

Since Mojave, you are no longer allowed to write to /. I suspect this is the cause of your problem: nothing to do with Sublime Text.

Pick another directory to save your files to, preferably in your home folder.

1. Once you make your document, go to File and click Save (or just press cmd+n).
2. Write the title of your document.
3. Right under the name there should be a little box that says Macintosh. You can click on it and change it to whatever file you prefer.

you must have left the save location as "macintosh". Basically this error means, that this "macintosh" folder is read-only. There is no issue like "sublime not having permission to write to the disk".

Just save to a usual folder and you would be gtg.

Make sure you save it to your project's folder and not just to the desktop or whatever is the default.