You can force Firefox to ignore the website settings and save all passwords, but you must then be extra vigilant about which passwords you save. Banking sites and the like will now prompt you to save the password, which you probably shouldn't do for them.
There was an easy fix for Firefox before version 4 (see this post), but there are a few hoops to jump through for the latest version. Firefox 4 packages all the necessary files into omni.jar in the program folder, which is a non-standard archive format that needs to be specially altered. Below are the directions from this comment:
0. Make a backup copy of omni.jar
1. Unzip the omni.jar (using either 7zip, Winrar)
2. Edit accordingly
3. Pack again using ZIP format + SFX option (Self-Extract)
4. Rename back to omni.jar
5. Launch Firefox!