When Valentine activated the thing that made everyone start killing each other and go all homicidal in Kingsman: The Secret Service, why wasn’t Eggsy affected at all? I never saw him be implanted with a chip and they never said that the bunker offered any type of protection. So why was he able to think clearly and not go crazy?
The 'crazy waves' are transmitted by mobile phones that have Valentine's SIM card in them, which he distributes under the guise of offering a free service. I presume the (audio?) signal they transmit has a relatively short range, but a lot of the world's population will be within a short distance of one or more phones.
I presume that Eggsy and Merlin, being aware of the plot, don't carry such phones. Also I imagine that the entire of Valentine's mountain hideout doesn't contain any such enabled phones or possibly have cellphone service at that location deep within a remote mountain. They make a big deal over having to get the WiFi password to get access to the internet, probably because there's no service at that location.