A long time ago TVs gave of dangerous x-rays. So, back in the day our parents were right when they told us that sitting to close is dangerous. The cardinal rules of radiation are time, distance and protection. Since our parents didn't make us wear lead vests protection is not relevant. If you double your distance from a radiation source twice the distance you decrees the intensity of the x-ray by 4.
Times are different now. TVs no longer give off dangerous x-rays... unless you have a really, really old one. So, they are not dangerous per say. Now, sitting to close does strain the eyes, and that's not good.