You can't for a few reasons:
1) If you want an imaged-based restore where the backup is a single disk image, you won't be able to since FAT32 has a 4GB max file size restriction.
2) A file-based backup won't work, since FAT32 doesn't support UNIX style ACLs (or NTFS ACLs for that matter, not that that's applicable here). This would mean that, assuming all of your files are < 4GB, none of the permissions would be preserved, meaning everything would be screwed up on a restore.
3) The FAT family doesn't journal, so it is susceptible to data corruption. This isn't as big of an impediment as the first two, but is certainly a reason why backup software manufacturers don't go anywhere near FAT32.
Suggestion: You could always split your external HDD into two partitions. One FAT32 or exFAT for cross-platform sharing and one HFS+ volume for your Mac backups.
Edit: As spiff correctly points out, if you want to boot from the external after you reformat it, make sure you use GPT and not MBR when creating the volumes.