In bbPress, only some user roles are permitted to post unrestricted HTML content. Other users can only use some basic set of HTML tags, and tags like UL, LI, DIV… will not work, and bbPress will save them as text, not HTML. Because of that, when you quote complex HTML content, tags normally not supported will be displayed as text, not HTML.
To fix this, you need to allow all user roles to use the expanded set of HTML tags. And to do that, open the GD bbPress Toolbox Pro Settings -> Various Tweaks -> Expand KSES allowed HTML tags and attributes -> Allowed tags list. Select box there have 3 options, first one is default bbPress set of HTML tags, and the other two include a wide range of supported HTML tags. You need to switch this option to second or third option.
But, there are some HTML tags that are not permitted (IFRAME, SCRIPT, STYLE) because in general, they can contain dangerous content, and when quoted, such tags will be escaped and saved as plain text. Because of that, quoting content that contains embedded content (FaceBook posts, Twitter tweets…), is not quotable.