Solution:
"In case you would like to exercise "localhost" for development, you should include it to the list of domains."
This will just perform in case you access localhost exercising 127.0.0.1/... rather than localhost/....
The real answer is preserved below.
"localhost domains are no longer approved by default. In case you wish to main supporting them for development you can include them to the list of adopted domains for your site key. Go to the admin console to update your list of adopted domains. We conference to employ a separate key for development and production and to not approve localhost on your production site key."
So only include localhost to your list of domains for your site and you'll be good.
"With the following test keys, you will always obtain No CAPTCHA and all verification requests will pass.
Site key:
6LeIxAcTAAAAAJcZVRqyHh71UMIEGNQ_MXjiZKhI
Secret key:
6LeIxAcTAAAAAGG-vFI1TnRWxMZNFuojJ4WifJWe
The reCAPTCHA widget will display a warning message to assertion that it's just for testing purpose. Please do not exercise these keys for your production traffic."
Update:
In case your question is how to set reCaptcha in Google site for exercising it in localhost, then i has been wrote it above however in case you are curious that how you can employing reCAPTCHA on both localhost and website host by minimal codes in your controller and prevent some codes like ConfigurationManager.AppSettings["ReCaptcha:SiteKey"] in it then I help you with this extra description and codes in my answer.
Employing these keys below, you can apply your tests on localhost, these keys are given in the above link for testing purposes by google:
Site key: 6LeIxAcTAAAAAJcZVRqyHh71UMIEGNQ_MXjiZKhI
Secret key: 6LeIxAcTAAAAAGG-vFI1TnRWxMZNFuojJ4WifJWe
Google includes a message on recaptcha to prevent users and the administrator that keys are only for tests.
