Okay a runner, runner flush is pretty rare (I think about a 1 in 20 chance). So on the surface, you shouldn't be too worried about losing to one.

However, I've noticed a trend of people making calls when the 2nd flush card falls on the turn because now they have more flush outs.

For example, villain has A[h] 7[h] and flop is A[c] K[d] J[h]. He foolishly calls a flop bet lets say. Turn is 5[h]. Bet is strong and he's going to call because now he knows if he hits his 3rd heart on the river, he's really going to take the other guys stack (implied odds).

So do you fear the runner, runner flush or pretty much ignore it (say you were guy putting pressure on the A7 guy).

Depends on the action up to that point and stack sizes.