To navigate to your invitation settings, open the Hangouts app on your phone or tablet, press the hamburger menu button, and select Settings > [your email address] > Customize invites (under “How others get in touch with you”).
The default seems to be that whenever someone new sends you a message in Hangouts, you will get an invitation to chat. However, you can now you can set different behaviors for people who have your email address, your phone number – and then anyone else.
For example, if someone already has your phone number, you can set it so that these people can contact you directly, with no invite needed. If someone already has your email address, you might leave it at the default setting, in which you’ll receive an invitation if they try to chat. If someone has neither, you can set it so they can’t contact you at all.
Additionally, Google has expanded the same functionality to your circles in Hangouts, so you can determine on a per-circle basis how you want Hangouts to respond for you.
These features are available right now, as long as you’re running the latest version of Hangouts. It is also available in the web version of Hangouts, and on iOS.