You say single issue, but really the NRA is single Amendment. They fight for a strong, individual right within the 2nd.
Privacy, unfortunately, doesn't have that same focus within the Constitution. Where the 1st gives, the 4th takes away esp with respect to National Defense. So Privacy advocates are left to fight a broad argument based on the protections in the 1st and by narrowing the definition of reasonable searches. That's a much harder problem and a long game that requires many, complementary actors.
Privacy, unfortunately, doesn't have that same focus within the Constitution. Where the 1st gives, the 4th takes away esp with respect to National Defense. So Privacy advocates are left to fight a broad argument based on the protections in the 1st and by narrowing the definition of reasonable searches. That's a much harder problem and a long game that requires many, complementary actors.