Do you have a link to the specific “Cloudflare Turnstile” plugin that you are utilizing? I’m asking because there appears to be several plugins that are available via the WordPress plugin directory.

Wordpress plugin : simple-cloudflare-turnstile

I should point out that in the settings for this plugin, the “BuddyPress Register” checkbox is checked. The captcha is also visible on all of my forms (contact, WordPress login, etc.).

I am looking for a way to add the captcha specifically to the “Members-only area” page.

The slug you provided corresponds to the Simple CAPTCHA Alternative with Cloudflare Turnstile plugin.

The simplest solution is to force BuddyPress to use the standard WordPress login form, this can be accomplished by utilizing the bp_view_no_access_redirect_to_login_screen filter hook with a callback that returns a value of true. A one-liner approach is as follows:

add_filter( 'bp_view_no_access_redirect_to_login_screen', '__return_true' );

Thank you for your help.

After thinking it over, I decided to create a small mu-plugin that automatically redirects people who are not logged in and try to access a restricted page to the login page.

This login page displays the correct captcha.

Kind regards