How to disable cropping of the site icon?

To force the site icon to be a specific attachment you can use the wp-admin/options.php page and search for the site_icon label then change the value of the field to the attachment ID you would like it to be.

Of course this also can be done via SQL, with a query somewhat similar to:

update wp_options set option_value=123 where option_name="site_icon";

Note that this only works once you initialized the site_icon option.