Not My Relative

No. Relativity applies always, but it might not need to be figured into calculations depending on the application and precision needed.

GPS makes use of the general theory or relativity while radar, particle accelerators for medical use and other applications depend on the special. Additionally, electromagnetism wouldnโ€™t even work if special relativity werenโ€™t true. I donโ€™t feel like typing out why now (as itโ€™s not very easy to understand) but Google will get you the answer to this at least.

This reminds me of Hertz, who discovered electromagnetic waves, but asserted that they were useless. (Hint for the smartphone people: itโ€™s how your smartphone works.)

People can believe the most absurd things. And do.