If the interlopers can do subconscious programming and even insert new beliefs, is this a clue that we should never stop examining the veracity of our own beliefs – no matter how fervently held?

Indeed, it is the case that subconscious programming can result in the insertion of new beliefs entirely—things never pondered, never held before by the person. In most cases, the manipulations are designed to exploit the current leanings, and this is in keeping with the strategy of divide and conquer. In other words, with political leanings polarized into two general ends of a spectrum, by inserting programming that appeals to both ends of that spectrum, there will be something that resonates for the person, and when they embrace those leanings being offered anew, this will increase the efficiency and effectiveness of the changes being sought to further polarize thinking and cement it in a more rigid fashion. This indeed would suggest all can profit from examining even their most cherished inner beliefs to see if they are still appropriate and serving what is highest and best for the individual.