How do I disable responsive images in WP 4.4?

Here are few things you could try to remove the responsive image support in 4.4:

/**
 * Disable responsive image support (test!)
 */

// Clean the up the image from wp_get_attachment_image()
add_filter( 'wp_get_attachment_image_attributes', function( $attr )
{
    if( isset( $attr['sizes'] ) )
        unset( $attr['sizes'] );

    if( isset( $attr['srcset'] ) )
        unset( $attr['srcset'] );

    return $attr;

 }, PHP_INT_MAX );

// Override the calculated image sizes
add_filter( 'wp_calculate_image_sizes', '__return_empty_array',  PHP_INT_MAX );

// Override the calculated image sources
add_filter( 'wp_calculate_image_srcset', '__return_empty_array', PHP_INT_MAX );

// Remove the reponsive stuff from the content
remove_filter( 'the_content', 'wp_make_content_images_responsive' );

but as mentioned by @cybmeta the problem may be elsewhere.

Force https on srcset

You could do some debugging with the wp_calculate_image_srcset filter and even try this quick-fix:

add_filter( 'wp_calculate_image_srcset', function( $sources )
{
    foreach( $sources as &$source )
    {
        if( isset( $source['url'] ) )
            $source['url'] = set_url_scheme( $source['url'], 'https' );
    }
    return $sources;

}, PHP_INT_MAX );

to set the url scheme to https. Another approach would be to have it schemeless //.

Check out the Codex for other set_url_scheme() options:

$source['url'] = set_url_scheme( $source['url'], null );        
$source['url'] = set_url_scheme( $source['url'], 'relative' );

But you should try to dig deeper and find the root cause.

Update:

We could bail out earlier from the wp_calculate_image_srcset() function with:

add_filter( 'wp_calculate_image_srcset_meta', '__return_empty_array' );

then using the wp_calculate_image_srcset or max_srcset_image_width filters.

Also updated according to ticket #41895, to return an empty array instead of false/null.