I think it's baked into a certain conservative mindset that
they are the ones who don't have anything to hide, which makes sense because if you don't have many progressive opinions then you probably aren't chafing against authority too often.
And, I think authoritarians (many of them seem to march under the "conservative" banner these days) are fine with surveillance because they see it as a hallmark of an effective authoritarian government, and again they see themselves as members of the "in" group. They want those subversives who are hiding things to be found and punished.
Unfortunately, I don't think any of these people will be terribly moved by the fact that leaders of progressive social movements in the past or present have been targeted by surveillance. Their world-views are shaped by a perception that they will not be targeted by an overreaching government, and such movements are comprised of their explicit political enemies.
However, I think we stand to win over a lot of people with a libertarian bent who might be turned off by an anti-surveillance movement strongly associated with modern leftism. To what degree we risk alienating those leftists, I have no idea.