How do I unset hook_field_storage_load()? I'm trying to unset hook_field_storage_load() and hook_field_storage_write() in hook_module_implements_alter() without success. Is there any other way to turn off those hooks?
TL;DR hook_module_implements_alter() is not invoked when mongodb_field_storage_field_storage_load() is needed. You cannot achieve what you are trying.

The function that invokes hook_field_storage_load() is field_attach_load(), which contains the following code.

// Invoke hook_field_storage_load() on the relevant storage backends.
foreach ($storages as $storage =&gt; $fields) {
  $storage_info = field_info_storage_types($storage);
  module_invoke($storage_info['module'], 'field_storage_load', $entity_type, $queried_entities, $age, $fields, $options);
}


module_invoke() calls module_hook(), which contains the following code.

  $function = $module . '_' . $hook;
  if (function_exists($function)) {
    return TRUE;
  }
  // A
  // If the hook implementation does not exist, check whether it may live in an
  // optional include file registered via hook_hook_info().
  $hook_info = module_hook_info();
  if (isset($hook_info[$hook]['group'])) {
    module_load_include('inc', $module, $module . '.' . $hook_info[$hook]['group']);
    if (function_exists($function)) {
      return TRUE;
    }
  }


Since mongodb_field_storage_field_storage_load() is contained in mongodb_field_storage.module, your implementation of hook_module_implements_alter() will not be called. In fact function_exists($function) returns TRUE when $function is equal to 'mongodb_field_storage_field_storage_load', and the part of the code after the line marked with // A will not be executed.