Check if user registered more than a month ago

You can try this:

/**
 * Is the current user registred for more than x days ago?
 * 
 * Based on the compare idea in this answer:
 * http://stackoverflow.com/a/7130744/2078474
 *
 * @link   http://wordpress.stackexchange.com/a/143597/26350
 * @param  int  $reg_days_ago
 * @return bool 
 */

function is_user_reg_matured( $reg_days_ago = 30 )
{
    $cu = wp_get_current_user();
    return ( isset( $cu->data->user_registered ) && strtotime( $cu->data->user_registered ) < strtotime( sprintf( '-%d days', $reg_days_ago ) ) ) ? TRUE : FALSE;    
}

This should return TRUE for users registred more than x days ago, and FALSE for visitors (not logged in) and other users.

Usage Example:

if( is_user_reg_matured( 30 ) )
{
    // show content
}

Shortcode:

You can for example add this as a shortcode:

[is_user_reg_matured reg_days_ago="30 ]

 Content for register matured users only

[/is_user_reg_matured]

with:

add_shortcode( 'is_user_reg_matured',   'is_user_reg_matured_shortcode' );

/**
 * Shortcode [is_user_reg_matured] to show content to register matured users only
 *
 * @link   http://wordpress.stackexchange.com/a/143597/26350
 * @param  array  $atts
 * @param  string $content
 * @return string $content
 */
function is_user_reg_matured_shortcode( $atts = array(), $content="" )
{
    $atts = shortcode_atts( 
            array(
                'reg_days_ago' => '30',
            ), $atts, 'is_user_matured' );

    if ( function_exists( 'is_user_reg_matured' ) )
        if( is_user_reg_matured( (int) $atts['reg_days_ago'] ) )
            return $content;

    return '';
}