BBcodes can be used in signatures. BBCodes are essentially the same as WordPress shortcodes, and they are processed the same way WordPress processes shortcodes. And, this can cause problems with signature editing.
If you make a shortcode that uses BBCodes, you can edit it through user profile on the admin side, through bbPress user profile edit page and through BuddyPress user profile edit page. The first method is not a problem and will always work as expected. But, the problem comes if you use bbPress or BuddyPress profile edit pages.
For bbPress and BuddyPress to be able to work with any WordPress theme, both plugins have something called ‘theme compatibility mode’. When the theme has full support for either bbPress or BuddyPress, the theme will have templates made for different types of pages for these two plugins. If that is the case, everything will be OK, and signature with BBCodes editing will work as expected.
But, if your theme doesn’t have direct support for bbPress or BuddyPress, these plugins will fallback to using theme compatibility. And that means that they will render own content and wrap it into page object, and then use theme page.php template to display. This will cause that all BBCodes in the rendered content will be processed by all standard theme content filters, including the one that will process shortcodes/BBCodes. And, raw BBCodes in the editor’s area will be processed also.
There is nothing plugins can do to prevent that. If you want to use BuddyPress or bbPress profile editors to edit signatures with BBCodes, that will work only if your theme has direct support for BuddyPress and/or bbPress. If the theme can work in compatibility mode only, this will not work.
To be able to edit BBCodes based signature in BuddyPress and/or bbPress profile editors, the theme needs to have direct templates support for these plugins.