Bertil_1939 said

Lately (couple of months) when I log-in I have to prove I am not a robot by identifying a lot of silly pictures with cars, traffic lights etc.

That's a Website function. Nothing FF 'added' or did. Perhaps reloading the page a number of time might show just a checkbox instead of playing the picture selection game, which I also do not like.

I don't know if a clever JavaScript code could make it easier or bypass this 'confirming' stage or not.

Otherwise, complain to the Webmaster of that site.

~Pj

Why then does the non-robot request not appear when I log-in with Chrome?

The 'I'm not a robot' captcha is powered by Google. When using Chrome, Google have collected enough information about you to conclude from your behavior, that you're actually human. Apparently they haven't collected that kind of behavioral information when you use Firefox. So you may consider this being good news. https://aibusiness.com/recaptcha-trains-google-robots/

Interesting, thank you. Who decides to use the Robot-captcha? If it is the web-site I want to access, they should be able to mark me as a accepted visitor - after all, I am a registrered customer. If it is the web-browser then Firefox should be able to do so, in order to stop me from switching to Chrome. Any other alternatives?

Who decides to use the Robot-captcha?

The owner of the website.

Any other alternatives?

I'd say it's a trade-off between convenience and privacy. You decide what's more important to you.