I have now added this plugin to my site: https://ww.wp.xz.cn/plugins/buddypress-captcha/
A lightwiehgt and easy to use plugin. It adds the Google reCaptcha field to the BuddyPress Sign-Up form.
(Google Account needed.)
Thank you, Shea, for you feedback.
Have a nice holiday season.
You were right, another framework implemented alongside to WordPress was conflicting with the Javascript of CF7. Disabling the CF7-JScripts highlighted the issue.
Thank you!
[resolved]