Btw, when did fj add recaptcha on login? Is it necessary to have recaptcha and 2FA together?
It is indeed a bit annoying to have recaptcha and 2FA at the same time, but as long as it is for more security reason then I think it is OK. Maybe FJ need to have an option to those who have activated 2FA so they can skip or remove the recaptcha. To be honest, it is not really a big problem for me because the biggest exchange in Indonesia that I use very often have one more security process which is an email verification. So there are 3 steps to login, recaptcha-email verification-2FA.
I am pretty sure the recaptcha has nothing to do with the site. Its usually mandatory if there is something off with your login credentials. For example if you got a new IP, got a new browser, new cookies, new windows version, etc.
Another reason can be if Google detects you logging into too many sites in a small period of time, usually it does this to prevent spam and fraud. If you logging in a similiar manner every few days, then you shouldn't get this issue most of the time.