Custom CSS based on the Author of a Post

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In your theme’s function.php, you can add this code:

add_filter('body_class', function($classes) {
    $classes[] = 'author-' . get_current_user_id();

    return $classes;
});

This will add a CSS class with the current author’s ID to <body> which you can then target:

.author-2 .widget_bt_claim_widget {
    display: none;
}

See https://developer.wordpress.org/reference/functions/get_current_user_id/ for return values.