How to Override CSS for a core module?
Ben Your solution is not ideal, as you now have your own version of the toolbar module, and should there be any bug fixes and security fixes, you will not benefit from those, without upgrading your version of the toolbar module.

Solution 1.

CSS will by it's design overwrite itself, since the theme CSS files will be included last, any rule you make in your theme that is identical to what's in the toolbar will take presedence.

Solution 2.

Sometimes it can be a pain to revert styles to browser default, if that is the case, creating a css file with the same name as the one you want to remove and including it in your theme, will make Drupal skip the one in the module and use the one in your theme. In this case creating a toolbar.css file anywhere in your theme and adding it in your info file, will remove the toolbar.css file from the toolbar module and fix your problems.
Remember to clear cache

Solution 3.

If by some reason you have problems making solution 2 work, you can instead remove the css file using hook_css_alter, this only works in Drupal 7+