How do I disable this awful two factor authentication, it is keeping me signed out of my devices and in an endless loop.

From the article below. If it has been on longer than 2 weeks, you can't turn it off. There has been some posts that state the article is no longer correct and now you can't turn it off, but I haven’t been able to verify that.

Can I turn off two-factor authentication after I’ve turned it on?

If you already use two-factor authentication, you can no longer turn it off. Certain features in the latest versions of iOS and macOS require this extra level of security, which is designed to protect your information. If you recently updated your account, however, you can unenroll for a period of two weeks. Just open your enrollment confirmation email and click the link to return to your previous security settings. Keep in mind, this makes your account less secure and means that you can't use features that require a higher level of security.

Apple ID -Two-factor authentication

https://support.apple.com/HT204915

What if I use two-factor authentication on a device running older software?

"If you use two-factor authentication with devices running older OS versions—like an Apple TV (2nd or 3rd generation)—you might be asked to add your six-digit verification code to the end of your password when signing in. Get your verification code from a trusted device running iOS 9 and later or OS X El Capitan and later, or have it sent to your trusted phone number. Then type your password followed by the six-digit verification code directly into the password field."

Also:

Jan 2017 Community Specialist sterling_r post: https://discussions.apple.com/message/31213055#message31213055 - "On older software, if you are not given a box to enter the verification code, you can simply put it immediately after your password. Note that this would not require a space."

What problems are you having signing into the Apple TV? If you are having problems entering the verification code, if you see a password box, enter the password (ABC) followed by the code (123) or ABC123.

Need Ask Admin to remove 2 step sign on. To

This is the way the 21st century is. I have a 38 year old car. It still works but since you can't get parts for it easily so it isn't our main vehicle. We have a 2016 car as well and I very much doubt it will still be around in 36 years. I also have a stable full of 10-20 year old devices but learning how to use them in this day and age -- and to accept that in some cases you cannot -- is an art in itself. Technology has made big changes in the past decade or two and the days when something lasted for 20 years are gone. No, I don't like it either but as long as people are demanding the fastest, lightest, super-3D, 4K, 5G, whatevers, that's the way it is.

As for the two factor thing, people are freaked out about privacy of data (of course they then post the same things on Facebook where everybody can see it). In using Apple services Apple is becoming part of that privacy, which then also includes privacy of Apple's things too. People are sloppy about security but then go complaining to Apple because their accounts have been "hacked" when they used Freedom as a password. So Apple has to come up with stronger security measures because if an account has been hacked it affects Apple's stuff too.

I don't have two-factor on my account and I'm surprised if you have old equipment that you have it. Apple keeps on trying to slip signing up for 2 factor into things I do such as setting up an iPhone SE I was given, but I know to keep an eye open for such things and maybe you didn't notice it unless you just set up your Apple ID. I also don't really do anything such as actually get anything from the iTunes or App stores for which I have to pay so they probably don't insist I have it.

Is the box you are entering the in a password type box or are there 6 individual entry boxes?

Reference your last paragraph, that has worked for some.

Or does Apple just want to force me to buy a newer model...?

And what model might that be?

https://support.apple.com/HT204915 --> What if I use two-factor authentication on a device running older software?

Did you try what I suggested above?

From the article.

What if I use two-factor authentication on a device running older software?

If you use two-factor authentication with devices running older OS versions—like an Apple TV (2nd or 3rd generation)—you might be asked to add your six-digit verification code to the end of your password when signing in. Get your verification code from a trusted device running iOS 9 and later or OS X El Capitan and later, or have it sent to your trusted phone number. Then type your password followed by the six-digit verification code directly into the password field.

Clarification question - are you entering the password followed by the code? If you only enter the code, it won't work.