Voters don't vote on particular decisions, or even on decision makers for particular issues, they vote on one decision maker for all issues.

How likely is it that an anti-surveillance candidate also happens to satisfy more than 50% of voters on aspects other than surveillance?

Since surveillance is low on the list of priorities of most people, it's a rational choice for them to ignore the candidates' stance on surveillance while choosing their preferred candidate.

As such, the stance of republican leaders on low-interest, non identity-defining aspects like surveillance is mostly unaffected by democracy.