Upgrade from 5.0.4 to 5.1.1 causes $theme to be null

When we upgrade from 5.0.4 to 5.1.1 the site stops loading.

The error message is

Fatal error:  Uncaught Error: Call to a member function images_path() on null 
/wp-content/themes/mytheme/header.php on line 49

Line 49 is
<?php $theme->images_path(); ?>

above it in the same file is
global $theme;

$theme is created in functions.php as the instance of our custom theme.

class MyTheme {
  private $theme_name = "MyTheme";
  private $scripts_version = '0.90';

  function __construct() {
    add_action('init', array($this, 'init_assets'));
    ...several of these
  ...more methods
  }
}
...other stuff
$theme = new MyTheme();

I don’t know how to troubleshoot this issue. Everything worked great prior to the upgrade and no other changes were made to the site.

Any help appreciated.

Since Changeset 44524, which has landed in WordPress 5.1, the variable $theme is now a global variable set by WordPress which also gets unset after the themes have been bootstrapped:

// Load the functions for the active theme, for both parent and child theme if applicable.
foreach ( wp_get_active_and_valid_themes() as $theme ) {
    if ( file_exists( $theme . '/functions.php' ) ) {
        include $theme . '/functions.php';
    }
}
unset( $theme );

This means that any value set by your theme gets also unset.

To fix the fatal error you now have to replace all variables named $theme with a prefixed version, for example $my_theme. Prefixing variables and functions in global scope is considered best practice to avoid such issues.