is there any way to keep free contributed plugin (for example MageMonkey 2) to be enabled across different instances of website(dev, stage, prod), keeping the configuration?

Suggested solution:

I've managed situation by adding required module to composer.json of my custom administrative module managing dependencies to another modules and adding UpgradeData.php with update script.

More detailed explanation:

Code structure

|--app/
 |--code/
 |--<My Vendor>/
 |-- ...
 |--<My Module>/
 |-- ...
 |--Helper
 |--Configuration.php
 |--Setup/
 |--UpgradeData.php # save custom module settings here
 |-- ...
 |--composer.json # module's composer file
|-- ...
|--vendor/
 |--<ContribVendor>/
 |--<ContribModule>/
|-- ...
|--composer.json # home directory composer file
|--auth.json # can be gitignored

Module composer.json sample

 "name": "<My Vendor>/<My Module>",
 "description": "N/A",
 "require": 7.0.2,
 "type": "magento2-module",
 "version": "<My Module version>",
 "license": [
 "OSL-3.0",
 "AFL-3.0"
 ],
 "autoload": 
 "files": [
 "registration.php"
 ]
 

Upgrade script sample:

<?php
namespace <MyVendor>UpdatesSetup;

use MagentoFrameworkSetupUpgradeDataInterface;
use MagentoFrameworkSetupModuleContextInterface;
use MagentoFrameworkSetupModuleDataSetupInterface;
use <MyVendor><My Module>HelperConfiguration;
class UpgradeData implements UpgradeDataInterface

 /**
 * @var <MyVendor><My Module>HelperConfiguration
 */
 protected $config;

 public function __construct(
 Configuration $config
 ) 
 $this->config = $config;
 

 /**
 * @inheritdoc
 * @SuppressWarnings(PHPMD.ExcessiveMethodLength)
 */
 public function upgrade(ModuleDataSetupInterface $setup, ModuleContextInterface $context)
 
 $setup->startSetup();
 try 
 if (version_compare($context->getVersion(), '<ModuleVersion>', '<=')) 
 $this->config->setMyModuleSettings(); # Implemented in HELPER below.
 
 
 catch (Exception $e) 
 print $e->getMessage();
 

 $setup->endSetup();
 
 

Helper script sample:

<?php
namespace FFWUpdatesHelper;

use MagentoConfigModelResourceModelConfig;
use MagentoFrameworkAppHelperContext;

class Configuration extends MagentoFrameworkAppHelperAbstractHelper 

 /**
 * @var MagentoConfigModelResourceModelConfig
 */
 protected $config;

 public function construct(
 Context $context,
 Config $config
 ) 
 parent::__construct($context);
 $this->config = $config;
 

 /**
 * Helper to set <My Module> settings.
 */
 public function setMyModuleSettings() 
 $this->config->saveConfig('<Config key according to schema.xml of module implementing config - ContribModule in our case>', <Value>, '<Scope>', '<ScopeId>');
 

Final step

I my CI i run 2 steps on each deployment - during development:

magento setup:upgrade
magento setup:di:compile

Disclaimer

Do not forget to add your api keys for contrib module to composer auth.json file (or any other authentication method for composer).