I don't even think the real reason is about potential risks, it's solely about the fear that an anti-smoker will see the plume and react as though it were smoking - probably not because they actually think it is (e-cigs have appeared in public and in the media enough now for people to not assume a cloud in a non-smoking area is smoke), but because they have been so brainwashed over the last 10 years or so that the mere sight of smoke will damage their health, then something that looks like smoke and has roughly the same effect on the user couldn't possibly NOT be bad for them.
Not only does this ignore the fact that there is actually no evidence that passive smoking is a health hazard (people just believe it because everyone has said it often enough, particularly a well-loved celebrity with lung cancer), but also simply feeds into this irrational hatred of all things related to nicotine use/smokers.
I've said it before, the anti e-cig attitude from the public stems from their hatred of smokers.
I've had two intense debates on trip advisor about vaping on planes, and it's full of people harping on about inhaling our nicotine. As research has shown little or no nicotine in the exhaled vapour, eating a potato salad would infect them with nicotine more than I could, but there's no rationality to work with in such debates.
As far as I'm concerned, as a business that invites me in to bring them custom, they have no moral right to prevent me from vaping, in exactly the same way that it would be unreasonable to tell me I couldn't chew gum or wear red. Generally, I aim to vape inconspiciously, but I'll be damned if Im going to ask to pursue a harmless and legal activity. If I'm ever asked to stop, I'll drink up and leave.
Landlords, managers and pub chains need to understand that the old smokers (the loss of whom since the smoking ban has closed many a pub) will return to the pubs if they can vape and a golden opportunity to revitalise the pub trade will be lost with these short-sighted and ill-informed decisions.