Real Homes theme supports Google reCaptcha for its forms. Google reCaptcha can be configured and enabled from Customizer > Misc options panel.
Once reCaptcha is configured and enabled it will be displayed on theme forms e.g: Contact Form, Agent Contact Form, and Login/Register Forms.
If you have configured and enabled the Google reCaptcha but still unable to display it on any supported theme’s form then ensure there is no other Google reCaptcha being rendered on the same page by any third party plugin or script.
Google reCaptcha allows only one API call on a page. If there are multiple API calls on the same page, it would result disabling other API calls after the first call.
To avoid this Google reCaptcha conflict you would need to disable the Google reCaptcha from third party plugin settings.
For any further help, you can create a ticket by clicking here (login required).