Use Custiomizer to setup meta theme color tag

Depending on whether you store your customizer settings as mods or options (which you define with the type parameter when adding a setting) you can simply use get_option or get_theme_mod in your header.php like this:

echo '<meta name="theme-color" content="' . get_theme_mod('my_browser_bar_color','#000000') . '">';

This line tells to look for the mod and if it isn’t there make the color black.

To make this work with js-driven live preview you will also have to add a piece of jquery that appends the line to the <head> tag.