Early monochrome TVs with lower voltage power supplies don't emit harmful amounts of X-Rays. Color and larger screens introduced higher and higher anode voltages, and they became quite effective producers of X rays. This was recognized as a health hazard, and beginning in the late 60s, TVs included a lot of shielding to block the X rays from leaving the set. There will be an X ray shield around the bell of the CRT, and the flyback and high voltage rectifier are fully enclosed. Provided all the shielding is in place, they were tested to produce an amount of X rays which wasn't harmful. A lot of media attention was focused on TVs and X rays around the time when standards for shielding were being introduced.
Another thing to remember is the intensity of x rays decays exponentially with distance, so sitting on your couch there is pretty much no risk with about any old TV.
The conclusion I take from learning about this issue, is that the only TVs you really need to be careful about, are those with safety features which have been defeated, or pre 1968 colour or projection sets with a high (>15kV) voltage on the anode of the CRT. For those sets, the idea would be to keep a distance. Also, if a TV loses high voltage regulation, and produces excessive high voltage, it can also produce excessive x rays, so only use TV sets which are in good operating condition.
There's many publications which talk about the issue of X rays and TV, and if you didn't find it already, I suggest using the resources at
www.americanradiohistory.com to search the various industry publications of the era for articles on the subject.