Final answer:
The controversial topic in question is 'c) Extraterrestrial encounters,' which is related to the 1947 UFO incident near Roswell, New Mexico, and the supposed government cover-up to hide evidence of alien life.
Step-by-step explanation:
The controversial topic associated with Southeastern New Mexico, a UFO crash, and Government Cover-Up is c) Extraterrestrial encounters. This refers to the famous incident that took place in 1947 near Roswell, New Mexico. Many people believe that an unidentified flying object (UFO) crash-landed in this area, and that the U.S. government then conducted a cover-up operation to hide evidence of extraterrestrial life. Though officially reported as a crashed weather balloon at the time, ongoing speculation, witness testimonies, and unofficial reports have fueled ongoing debate and interest, making it a cornerstone of UFO conspiracy theories.