Is it possible to make shortcodes NOT case sensitive?

Here is another simple idea for a case-insensitive shortcode:

/**
 * Make a shortcode case insensitive via the the_content filter
 *
 * @param string $content
 * @return string $content
 */
function my_case_insensitive_shortcode( $content )
{
    $sc="test"; // Edit this shortcode name to your needs

    $from = '['. $sc ; 
    $to   = $from;

    if( stristr( $content, $from ) )    
        $content = str_ireplace( $from, $to, $content );

    return $content;

}

add_filter( 'the_content', 'my_case_insensitive_shortcode', 10 );

You could also use preg_replace(), if you need more accurate replacements.

Example:

Writing this in the post editor

[test id="1"]

[tEsT id="2"]

[TeSt id="3"]

gives the following output before the do_shortcode filter is activated with priority 11:

[test id="1"]

[test id="2"]

[test id="3"]