"The external disk must be erased before it can be used for Time Machine backups because it has an incompatible filesystem." What if I don't want to erase the disk?

Time Machine must back up to a hard drive that has been formatted in Mac OS Extended (Journaled). Your drive is likely formatted in FAT 32.

If you want to use the drive for Time Machine backups, you will have to erase it and reformat using Disk Utility on your Mac.

First, move the files that you do not want to lose to another temporary location and test to make sure they are OK.

Second, erase the drive that you want to use for Time Machine backups and format it for Mac OS Extended (Journaled).

Third, move the files back to the hard drive. Test to make sure they are OK. When you are sure that the files are safe, you can erase them from their former "temporary" location. (Although I do wonder how you are backing up these files).

Time Machine will not touch the other files that you have on the hard drive.

If you do not have temporary space, you do already have backups for these files on another drive, corrrect? 😉

If not, you already know what you must do.....if these files are valuable.