In my experience it's not people that are worried about getting sick. It's that they just don't like eggs that much and raw eggs are even worse. So the idea of plopping an egg white into a delicious whiskey sour makes them want to gag.

I have one convert so far, but he didn't see me make the drinks, just the final result.

I'll have to try chickpea juice though since it seems logistically easier than dealing with an egg for a drink.