If the drive is formatted FAT32 then there is no way around it. Time Machine will not be able to backup the drive. You would have to repartition and reformat the drive for OS X, but that will make it unusable on a PC. You should try using a third-party backup utility if you cannot reformat the drive:
Backup Software Recommendations
If you backup to the same drive used for your Time Machine backup, then you should create a separate partition on the drive for these backups.
I am trying to back up an external hard drive with Time Machine, but in Options, the drive is greyed out and cannot be removed from exclusions.
The drive must be formatted in Mac OS Extended (Journaled) to work with Time Machine.
I read that it cannot back up Fat32, if that is true, how do I work around that? My Aperture library is on this drive.
You will have to move the Aperture library to another location for temporary storage. Then format the drive for Mac and move the library back to the drive.
Once this is done, Time Machine will backup both your Mac and the external hard drive.
by moving the Aperture library, will that cause issues at all when I reopen the program? Will it have to re-index all of the files
That is a question for the guys over in the Aperture forum. I've done this with iPhoto libraries and there are no issues at all, but I have not used Aperture.
I imagine that you will have to "point" the Aperture application to the "new" location of the library on the external hard drive once it has been re-formatted and the library has been moved back over.
At least that is the way that it works with iPhoto....you hold down the option key on your Mac while starting the iPhoto application and simply point to the location of the library. After that, iPhoto knows where the library is located and will open it automatically when the application starts.