Issue adding featured image option to functions.php

As user /u/majick suggests in the comments below: the better option may be after_setup_theme which looks like this:

function theme_setup() {
    add_theme_support( 'post-thumbnails' );
}
add_action( 'after_setup_theme', 'theme_setup' );

Another options is to use init.

function theme_init() {
    add_theme_support( 'post-thumbnails' );
}
add_action( 'init', 'theme_init' );

The init hook explicitly states:

Fires after WordPress has finished loading but before any headers are sent.