It appears that Google Captcha does not seem to work with the GDPR extension.
I have a fully working setup using profiles as normal on site - which can be seen here
https://peoples-press.com/index.php?option=com_civicrm&task=civicrm/profile/create&gid=57
However, on this form,
https://peoples-press.com/index.php?option=com_civicrm&task=civicrm/gdpr/comms-prefs/update
I have captcha activated but it does not show on form. If I click Save then it alerts me to complete Captcha despite it not being possible. Form works fine if I deactivate Captcha.
Joomla 3.8.7 and Civicrm 5.1