Summary (*)

Creating a store inside integration tests doesn't work if there is a plugin defined for Magento\Framework\App\Config.

I have a test that requires a new store and it is not possible to save it. There is an exception "Property data does not exist".
When saving a store, method \Magento\TestFramework\Store\StoreManager::reinitStores is called, the reflection class will only have properties from the Interceptor class and not \Magento\TestFramework\App\Config.

PHP: 7.0
Magento: 2.2.6

Examples (*)

Create a plugin for Config, doesn't matter what it does:

<type name="Magento\Framework\App\Config">
        <plugin name="some_plugin" type="Some\Vendor\Plugin\FrameworkAppConfig" />
</type>

Have an integration test that creates a new store:

$store = \Magento\TestFramework\Helper\Bootstrap::getObjectManager(\Magento\Store\Model\Store::class)->create();  
$store->setCode('new_store)->setWebsiteId(1)->setGroupId(1)->setName('New store')->setIsActive(true);  
\Magento\TestFramework\Helper\Bootstrap::getObjectManager(\Magento\Store\Model\ResourceModel\Store::class)->save($store);

Proposed solution