Thanks for the hint. Here is working solution without a direct return from the callback function:

    <?php
function remover_gender_init() {
    ossn_add_hook('user', 'default:fields', 'remove_gender');
    ossn_register_callback('action', 'load', 'replace_genders_male');
    ossn_register_callback('action', 'load', 'ensure_language_saved');
}

function replace_genders_male($callback, $type, $params) {
    if (in_array($params['action'], ['user/register', 'admin/add/user', 'profile/edit', 'admin/edit/user'])) {
        ossn_set_input('gender', 'male');
    }
}

function ensure_language_saved($callback, $type, $params) {
    if (!in_array($params['action'], ['profile/edit', 'admin/edit/user'])) {
        return;
    }

    $language = input('language');
    if (!empty($language) && in_array($language, ossn_get_available_languages())) {
        $user = ossn_loggedin_user();
        if ($user && $user->data->language !== $language) {
            $user->data->language = $language;
            $user->save();
        }
    }
}

function remove_gender($hook, $type, $fields) {
    // Check if the fields array has a 'required' or 'non_required' key
    if(isset($fields['required']) && is_array($fields['required'])) {
        foreach ($fields['required'] as $index => $field) {
            if ($field['name'] == 'gender') {
                unset($fields['required'][$index]);
            }
        }
        $fields['required'] = array_values($fields['required']);
    }

    if(isset($fields['non_required']) && is_array($fields['non_required'])) {
        foreach ($fields['non_required'] as $index => $field) {
            if ($field['name'] == 'gender') {
                unset($fields['non_required'][$index]);
            }
        }
        $fields['non_required'] = array_values($fields['non_required']);
    }

    // Use ossn_unset_hook instead of returning
    ossn_unset_hook('user', 'default:fields', 'remove_gender');
    ossn_add_hook('user', 'default:fields', function($hook, $type, $fields) {
        return $fields;
    });

    return $fields;
}

// Register the initialization function
ossn_register_callback('ossn', 'init', 'remover_gender_init', 1001);
?>

Callbacks must not return anything it will make others callbacks stop working

I have found a solution:

    <?php
function remover_gender_init() {
    ossn_add_hook('user', 'default:fields', 'remove_gender');
    ossn_register_callback('action', 'load', 'replace_genders_male');
    ossn_register_callback('action', 'load', 'ensure_language_saved');
}

function replace_genders_male($callback, $type, $params) {
    if (in_array($params['action'], ['user/register', 'admin/add/user', 'profile/edit', 'admin/edit/user'])) {
        ossn_set_input('gender', 'male');
    }
}

function ensure_language_saved($callback, $type, $params) {
    if (!in_array($params['action'], ['profile/edit', 'admin/edit/user'])) {
        return;
    }

    $language = input('language');
    if (!empty($language) && in_array($language, ossn_get_available_languages())) {
        $user = ossn_loggedin_user();
        if ($user && $user->data->language !== $language) {
            $user->data->language = $language;
            $user->save();
        }
    }
}

function remove_gender($hook, $type, $fields) {
    $toremove = array('gender');
    return ossn_remove_field_from_fields($toremove, $fields);
}

ossn_register_callback('ossn', 'init', 'remover_gender_init', 1001);
?>

Very useful component, unfortunately you can no longer change the language in the profile once you activate it.

For completeness, yes - it removes genders from the profile page too.

Is it possible to remove the gender in peoples profiles too?