added a comment - - edited
Similar problem occurs when all site is running on HTTPS and the setting "Use HTTPS for logins" (loginhttps) is not set. Then the reCAPTCHA image is loaded with HTTP and some browsers don't like that.
Choosing the "Use HTTPS for logins" fixes this one.
True, the text under this setting is confusing:
Turning this on will make Moodle use a secure https connection just for the login page (providing a secure login), and then afterwards revert back to the normal http URL for general speed.
– like the ohter site would switch to HTTP if I choose this (even when all site is running on HTTPS). Actually it does not.