After installation, it required me to load the mod to get it to work.
This is a safety precaution. Almost all mods (pretty much everything that's not graphics only) will render savegames invalid, due to their different structure. To avoid major hiccups, savegames "remember" their original mod (or non-mod).
If you want to install a graphics-only mod and keep your old saves working, you can install the mods as CustomAssets instead. To do so, locate the mod in your BtS mod folder, open the mod folder, open the "Assets" folder and copy everything in there.
Then go to your ...\My Documents\My Games\ folder, there should be a folder called "Beyond the Sword", open it. Then you should see a folder named "CustomAssets", if not, create one. Open the CustomAssets folder and paste the files in here.
This will
change your standard BtS game, allowing you to load your old savegames regularly. Note that if you use anything else but graphics-only mods (and by that, I really mean modified graphics only - things like ethnic unit art *add* new graphics and break stuff.. again), you'll get corrupted saves.
If you want to undo the changes, just delete the "CustomAssets" folder again. Note that Blue Marble (if you used the installer) uses this method by default, so don't be surprised, if there are files already.
And for your Fallout 3-complaint: That's the price for the higher moddability of Civ4 - you can do complete changes that invalidate savegames, that's a bit of inconvenience, but also added flexibility/power for the modders; hence things like FfH or Dune Wars were possible.
EDIT: @Baldyr: using the CustomAssets is a lot better than modding the gamefiles themselves, since you can't accidentally overwrite original files. CustomAssets don't work with modified themes and DLLs, though.
Cheers, LT.