Relativity doesn't come up until third semester of physics, typically, which is usually only for physics majors and certain kinds of engineers. Unless they're exposed to it through a particular curiosity or a show, it's not really common knowledge even in the sciences. However, those in the sciences are often the kinds of people who will have those curiosities and seek it out themselves.
Everything before that is considered Galilean/Newtonian as far as mechanics goes, depending on what you're doing, which are far more intuitive, but also generally poorly understood by the public as well.
E: I've had to teach it once or twice. Basically, quite a few students are blown away by some of the weirder parts of it because it's weird and entirely new, and some are just "meh" because they sought it out months ago. (I read Einstein's Relativity when I was a wee freshman yet to take a physics course, just out of curiosity.)
EE: Also, when discussing energy, that all really falls under the Conservation of Energy rather than relativity itself. Relativity focuses on proper treatment of the laws of physics in wonky inertial frames and plays with Lorentz transformations and the like.
EEE: I may correct people when it comes to science stuff, but I'm not trying to be a jerk. It is quite refreshing to see members of the general public give half a damn about science. Pseudoscience, new age-y bullshit, and the general tendency to embrace ignorance actually pretty much depress the hell out of me as a scientist.
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Gone.
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