okay this is just so you can see what I'm talking about. This is how its been in my games, for as long as I can remember, and its the easiest and quickest way for
me to know which cities I can join workers/settlers to.
I tried and tried to get workers/settlers to join Red cities but have never been able to. I used to run that worker/settler through every city trying to get to a city that "he" could join.
I do stand corrected on the "Yellow cities" though. You can add a worker/settler to some yellow cities (i.e. if it has the aqueduct/hospital/river etc.), but if the city is yellow, and you add a worker/settler you will turn it "red" thus it is going to "decrease" in size. So would it be worth adding that worker/settler?
What I've noticed is that it doesn't matter if you have aqueducts/hospitals etc. if you can't add the worker it will be red...so if there is no hospital at size 12 "red" city you will not be able to add the worker...Makes it easier than running that worker to every city to see if he can be joined. I just look for cities in "White" and know that I can safely join them there.

It's worked for me every time

(I don't add workers/settlers to yellow cities as it will turn them "red" and thus the city will decrease in size, I just don't see the use adding them if the city will then decrease)
Hope this works

first time posting images...
(Thank you Turner_727 for the help)
"White City" notice that the "join" icon is there, I was able to join this worker by either the icon or the "b" key
"Red City"notice that the "join" icon is NOT there, I was not able to join this worker by either the icon or the "b" key