Cannot connect to apple ID on older devices (Macbook Pro mid-2012 on OSX 10.9.5 Mavericks and Ipod Touch 5th generation)

This is a shared family apple ID. The password was changed on a newer device, and now older devices (Macbook Pro mid 2012 on OSX 10.9.5 Mavericks and a 5th generation Ipod touch, and others) can no longer login to apple ID, it always claims it's the wrong password, despite inputting the correct password (100% sure, thoroughly checked can login on newer devices and on this browser...) . I suspect this is due to 2-factor authentication being systematically required for new logins, and these devices not seemingly supporting the feature.

This is a potentially HUGE problem for older devices, and if it is due to the 2-factor authentication there may be no way around it unless apple patches things?

I can no longer redownload apps on my IPod or buy music on Itunes on my Mac. I potentially cannot update my Macbook Pro to a newer OS to solve the problem now either, because it seems to always require using the App Store??? I know I probably should have done it earlier, but I expected to be warned about this sort of fundamental compatibility issue arising...