If you've already updated your site to WordPress 4.8, then you may have been surprised to learn that the Classic Text Widget has been replace with a new Text Widget that uses the TineMCE Editor, the same editor that is used to edit posts and pages. While this is an improvement in that your content can now be displayed as rich text, it is a step backwards because all of the markup we've been able to use in the text widget before is now subject to the editor's code rewriting process, which includes auto paragraph tags and stripping HTML tags. If you never edit the code in your text widget, you'll be okay. The text widget only rewrites your code if you edit the widget's content. This article explains the expected issues with the new widget: https://make.wordpress.org/core/2017/05/23/addition-of-tinymce-to-the-text-widget/
Thanks to Christina Arasmo Beymer, the Classic WordPress Text Widget is available as a plugin. Christina started the work yesterday and uploaded her code to Github. She asked that someone fork the code and finish it up so it can be posted to the WordPress repository, which I've done. While we're waiting for its approval to the repository, you can download the plugin here: Classic Text Widget, or get the source code from https://github.com/vfontjr/classic-text-widget
Also check out Christina's article on how to bulk update the new text widget to the old classic version: https://christinacreativedesign.com/how-to-bulk-replace-the-4-8-wordpress-text-widget-with-the-classic-text-widget/