I had the same problem... I changed my YouTube password to something without numbers and symbols and it started working.
I just submitted the below to the Apple bug department.
Good luck,
Tenley
I do not think the Apple TV can recognize some symbols in YouTube passwords. (And maybe other account passwords?)
Today I bought an Apple TV. I set it up fine and linked my Apple ID, Netflix, home computers, iPad, etc. Everything worked. Then I tried to link my YouTube account...
I kept getting an error on Apple TV saying my YouTube login was incorrect. I tried the password multiple times but kept getting the error. I was able to login to my YouTube account with my PC, iMac, and iPad, but for some reason Apple TV was not working. My spouse verified that I was typing the password correctly.
My password was something like this: High&goodbye5757
(That is not the real password but follows the correct format.)
I called Apple Support and then had me restore the Apple TV. That did not fix the problem.
Then I changed my YouTube password to "aaabbbcccddd" and suddenly it worked. (Then I changed it to something more secure - but not using any symbols - and that worked too.)
I think the problem is that Apple TV cannot send symbols like "&" to YouTube (and other accounts?). That seems to be the reason it was not working because when I did not use "&" in my password, it worked fine.
Perhaps you can check your code to ensure Apple TV is correctly transmitting the "&" symbol.
Thank you.