While you can change the color under Preferences>User Interface, there is no way to delete the button itself. It is so that you can share your files for review and comment. You might have other ways to do so, but this is a new and useful way that is being added to the Adobe platforms.
Thanks for reaching out. Would you mind trying to change the appearance of the Share button from Preferences > User Interface to "Match Brightness" and checking if it helps?