It depends on your server. You may be able to add a line to your .htaccess file, if it's using an Apache module for PHP
php_flag register_globals Off
Be careful; you may also need to turn off magic_quotes_gpc, as this will cause extra / characters to be added to all quote marks in data saved to the database if it's on.
If you are using PHP as a CGI instead of an Apache module, you'll need to have a custom php.ini file in the site's root and the /manager directory with the necessary directive. The proper way to do this is to have a full copy of the default php.ini file with the desired changes added, but a file with just the required directives will do the job. Such a custom file needs to be in every folder that has a .php file that is run; MODx only actually runs two, the root index.php for the front-end and the index.php file in the /manager. All the rest of the MODx .php files are included by those two, so only those two directories need a custom php.ini file, unless you have custom AJAX scripts or something of the sort being run.
It's actually a very bad practice of your hosting to have either of these set to ON. They are being deprecated by PHP and most likely won't even exist in the next major version, since register_globals can cause security problems, and magic_quotes is not very good at adding any security, mostly only providing a false impression of doing so and otherwise just causing problems for properly written code that is secure.