Taking right value from the existing and new. DIRECTION: Activate one block per page load, and see the changes.

array.php

<?php
echo '<h3>1st time</h3>'; //===================================== 1st
$existing_locations = null;
$new_locations = array( 1,2,3 );				//+3 (1,2,3)

if( is_array( $existing_locations ) ) {
    $new_diff       = array_diff( $new_locations, $existing_locations );
    $existing_diff  = array_diff( $existing_locations, $new_locations );
} else {
    $new_diff       = $new_locations;
    $existing_diff  = $existing_locations;
}

if( $new_diff ) {
    foreach( $new_diff as $new_location ) {
        //add_post_meta( $post_id, "{$project_prefix}post_locations", $new_location );
        echo "New Multiple: ", $new_location, ' (', gettype($new_location) ,')', '<br>';
    }
}

if( $existing_locations && $existing_diff ) {
    if( is_array( $existing_diff ) ) {
        foreach ( $existing_diff as $existing_location ) {
            //delete_post_meta( $post_id, "{$project_prefix}post_locations", $existing_location );
            echo "Delete Multiple: ", $existing_location, ' (', gettype($existing_location) ,')', '<br>';
        }
    } else {
        //delete_post_meta( $post_id, "{$project_prefix}post_locations", $existing_diff );
        echo "Delete Single: ", $existing_diff, ' (', gettype($existing_diff) ,')', '<br>';
    }
}
echo '<hr>';


echo '<h3>2nd time</h3>'; //===================================== 2nd
/*$existing_locations = array( 1,2,3 );
$new_locations = array( 1,2 );				//-1 (3)

if( is_array( $existing_locations ) ) {
    $new_diff       = array_diff( $new_locations, $existing_locations );
    $existing_diff  = array_diff( $existing_locations, $new_locations );
} else {
    $new_diff       = $new_locations;
    $existing_diff  = $existing_locations;
}

if( $new_diff ) {
    foreach( $new_diff as $new_location ) {
        //add_post_meta( $post_id, "{$project_prefix}post_locations", $new_location );
        echo "New Multiple: ", $new_location, ' (', gettype($new_location) ,')', '<br>';
    }
}

if( $existing_locations && $existing_diff ) {
    if( is_array( $existing_diff ) ) {
        foreach ( $existing_diff as $existing_location ) {
            //delete_post_meta( $post_id, "{$project_prefix}post_locations", $existing_location );
            echo "Delete Multiple: ", $existing_location, ' (', gettype($existing_location) ,')', '<br>';
        }
    } else {
        //delete_post_meta( $post_id, "{$project_prefix}post_locations", $existing_diff );
        echo "Delete Single: ", $existing_diff, ' (', gettype($existing_diff) ,')', '<br>';
    }
}
echo '<hr>';*/


echo '<h3>3rd time</h3>'; //===================================== 3rd
/*$existing_locations = array( 1,2 );
$new_locations = array( 1,2 );				//0

if( is_array( $existing_locations ) ) {
    $new_diff       = array_diff( $new_locations, $existing_locations );
    $existing_diff  = array_diff( $existing_locations, $new_locations );
} else {
    $new_diff       = $new_locations;
    $existing_diff  = $existing_locations;
}

if( $new_diff ) {
    foreach( $new_diff as $new_location ) {
        //add_post_meta( $post_id, "{$project_prefix}post_locations", $new_location );
        echo "New Multiple: ", $new_location, ' (', gettype($new_location) ,')', '<br>';
    }
}

if( $existing_locations && $existing_diff ) {
    if( is_array( $existing_diff ) ) {
        foreach ( $existing_diff as $existing_location ) {
            //delete_post_meta( $post_id, "{$project_prefix}post_locations", $existing_location );
            echo "Delete Multiple: ", $existing_location, ' (', gettype($existing_location) ,')', '<br>';
        }
    } else {
        //delete_post_meta( $post_id, "{$project_prefix}post_locations", $existing_diff );
        echo "Delete Single: ", $existing_diff, ' (', gettype($existing_diff) ,')', '<br>';
    }
}
echo '<hr>';*/


echo '<h3>4th time</h3>'; //===================================== 4th
/*$existing_locations = array( 1,2 );
$new_locations = array( 1,2,5 );				//+1 (5)

if( is_array( $existing_locations ) ) {
    $new_diff       = array_diff( $new_locations, $existing_locations );
    $existing_diff  = array_diff( $existing_locations, $new_locations );
} else {
    $new_diff       = $new_locations;
    $existing_diff  = $existing_locations;
}

if( $new_diff ) {
    foreach( $new_diff as $new_location ) {
        //add_post_meta( $post_id, "{$project_prefix}post_locations", $new_location );
        echo "New Multiple: ", $new_location, ' (', gettype($new_location) ,')', '<br>';
    }
}

if( $existing_locations && $existing_diff ) {
    if( is_array( $existing_diff ) ) {
        foreach ( $existing_diff as $existing_location ) {
            //delete_post_meta( $post_id, "{$project_prefix}post_locations", $existing_location );
            echo "Delete Multiple: ", $existing_location, ' (', gettype($existing_location) ,')', '<br>';
        }
    } else {
        //delete_post_meta( $post_id, "{$project_prefix}post_locations", $existing_diff );
        echo "Delete Single: ", $existing_diff, ' (', gettype($existing_diff) ,')', '<br>';
    }
}
echo '<hr>';*/


echo '<h3>5th time</h3>'; //===================================== 5th
/*$existing_locations = array( 1,2,5 );
$new_locations = array( 1,5,4,7 );				//-1 (2), +2 (4,7)

if( is_array( $existing_locations ) ) {
    $new_diff       = array_diff( $new_locations, $existing_locations );
    $existing_diff  = array_diff( $existing_locations, $new_locations );
} else {
    $new_diff       = $new_locations;
    $existing_diff  = $existing_locations;
}

if( $new_diff ) {
    foreach( $new_diff as $new_location ) {
        //add_post_meta( $post_id, "{$project_prefix}post_locations", $new_location );
        echo "New Multiple: ", $new_location, ' (', gettype($new_location) ,')', '<br>';
    }
}

if( $existing_locations && $existing_diff ) {
    if( is_array( $existing_diff ) ) {
        foreach ( $existing_diff as $existing_location ) {
            //delete_post_meta( $post_id, "{$project_prefix}post_locations", $existing_location );
            echo "Delete Multiple: ", $existing_location, ' (', gettype($existing_location) ,')', '<br>';
        }
    } else {
        //delete_post_meta( $post_id, "{$project_prefix}post_locations", $existing_diff );
        echo "Delete Single: ", $existing_diff, ' (', gettype($existing_diff) ,')', '<br>';
    }
}
echo '<hr>';*/