They don't
If there is a big enough society and some people have started developing anything paranormal, there are two possible outcomes: first, those people display great control and self-discipline, and don't show off, and second, someone does show off and the information leaks out that there are mind readers out there!!!11 Our society is big enough for this purpose, and gossips of various paranormal activities do spread occasionally. (Whether there are grounds under those gossips is different story)
Next, if the first obstacle still didn't produce a worldwide gossip of mind readers being around, there are more. The second obstacle is that once a person gets some superpowers (and reading others' minds is one), they start using it and adapting their behavior to rely on those powers. So, eventually any mind-reader would start going with mind reading left and right. Eventually, one of them would lose self-control hard enough for "non-mind-readers" to notice, alerting the society that people's minds are no longer safe.
Next, even if all the present mind readers would retain their abilities in secret, two mind readers would eventually meet, and all of a sudden their ability would break when they'd try to read each other's minds. This would shock them both to a degree of either someone else seeing them shock at something, or them disclosing their abilities at least to their would-be victims. Even if only one person would try to read another mind reader's mind and fail per your ability description, they would definitely try to discern what is so different about that person as why they couldn't affect them. Such stalking behavior would eventually occur anyway, because people's psychology and law of big numbers say this can happen so it eventually will. Then, some neighbors would notice a mind reader stalking someone else, arising interest, and some of those readers would eventually lose control enough to disclose their ability. Say, when drunk.
Next, the rule of not discussing mind reading has to appear somehow. It's not a given, or say God-given rule. Someone has to devise a rule about not talking about their powers once encountering another person with these, but this rule won't appear before it would become obvious that breaking it would produce a highly undesirable outcome. The mind readers can't just meet and produce the rule before something would happen. At first they wouldn't even know why they can't read some people's minds so they have to speak about their superpowers at least with each other (or like with the first two, saying this the very first time would be psychically hard for either), so organizing into a "cult" or something like it would pose serious problems. Without organization, the rule wouldn't appear, so again, information disclosure would be required for it to appear.
Next, if all of the above won't alert the society about mind readers, there is a power problem. When the number of mind readers would become large enough, there will arise a selfish person who would use mind reading powers to elevate his position in the society, eventually rising high enough to influence the government somehow. Probably up to the position of a local ruler, superseding existing ruler if he'd be susceptible to mind reading. The story of his rise would get written and spread, as people like to write stories of their kings or other rulers that bring glory to their people (of whatever kind), and some of the brighter minds would at least suspect that the "from zero to hero" kid has some supernatural abilities. Also if somehow a child in the ruling family would get such a power, they would be plain forced to use it or perish, thus with the society you describe most of the power positions would eventually be filled with mind readers.
Then, since the rulers would eventually be aware of people that are unaffected by their mind reading abilities, there would be activity directed to study such people, with some selection initiated by the scientists or ruling mind readers themselves designed to gather such people. But then, there is a dilemma on who to send to gather such people! If the king, provided he is a mind reader, would go himself, others would start worrying both about his safety and about how would he find people he needs, effectively leaking data to any other mind reader around (aka the target). Sending "normal" people would fail, because they won't be able to find who is a mind reader and who is not, and also be an open book about the king's desires to find more of "people like other kings", after that it won't take long for the mind readers under that king's rule to organize. Once there is an organization, separation would take place, people with mind-reading immunity would be taken from those vulnerable, maybe other measures would be implemented, arousing the "normal" society about something is going on with some of them.
Then, as if everything above isn't enough, those kings would start taking care of their secrets, not knowing who to send on a secret mission without it becoming known to everyone who would listen, especially if one mind reading king would meet an aspiring hero that would desire to supersede him, capture him and interrogate (aka torture for information). So, if a cult of "special" people would not form amidst ordinary people, it will form as some kind of aristocracy by a willing king. Mind readers would eventually start being promoted to secret keepers or performers of secret tasks everywhere, new people would get elevation because of their ability, provoking "segregation by mind". Eventually some people from above would dissent and disclose the existence of mind readers to everyone else in order to undermine their opponents' ability to rule with reading minds of unawares, again leading to information disclosure.
Thus, the situation you describe is plain impossible. The information of people being able to read minds will at least be known to governments mostly because over the history all of them would contain mind readers and only mind readers. And eventually it will become known to everyone because of dissidents from either side.