Hi :) you are actually all wrong as it happens.
BBCode as we use in posts does work in usertitles (for supporters). However, there are a few bugs with how it's parsed that don't happen in other contexts. In this case the issue you're running into is that the quotes from the [color="#fff"] tag are being turned into ", which is the HTML-escaped version.
You can fix this by just removing the quotes! BBCode tags don't actually need them, usually. The following will work for you.
[color=#fff]Askr's Sword[/color]
In the future we'll be doing a major rewrite of the BBCode internals that will hopefully fix this and other issues.