Google's John Mueller emphasizes the significant impact of user interface (UI) and user experience (UX) changes on a website's SEO. UI involves elements like navigation, forms, and icons, while UX encompasses broader considerations such as accessibility, design consistency, mobile responsiveness, readability, and site speed. Both aspects influence user satisfaction and, consequently, SEO rankings. Mueller advises careful planning before implementing site-wide changes, urging a pre-change crawl using tools like Screaming Frog to identify potential issues. Creating multiple backups and staging the website for review before going live are crucial steps to mitigate risks and ensure a smooth transition. Staging allows developers to address technical bugs and errors before impacting the live site, emphasizing the importance of a thoughtful approach to website revamps.