I agree somewhat with what keyzygirl says in terms of coming across as polite. I also agree that any owner of property has a right to include or exclude any person or practice from that property at his/her sole discretion on any basis whatsoever, even if that basis is stupid. If I owned a restaurant, it would be my right, IMO, to make it only available to left-handed Ethiopian same-sex female couples who vape. I'd probably go out of business in a hurry, but it would be my right.
So yes the restaurant manager has a right to exclude anything that "looks like" smoking.
But along with rights come responsibilities and consequences. In my hypothetical restaurant if I am in the middle of Wyoming where Ethiopians are relatively rare, the consequences to my restrictions would include going out of business. I have the right to be stupid, but also must bear the responsibility of my folly.
I like Twisty's approach -- because it is an approach that very clearly connects rights and responsibilities. If I never show up at a restaurant because I already know they won't appreciate my 808 or 510, they have no idea what they lost. IT allows them to suffer from the illusion that their choice entails no loss.
If, on the other hand, they exercise their choice to prohibit my use of a HARMLESS device -- certainly something less harmful than the carcinogens put in the air from braising a steak -- and I then exercise MY choice to walk out ... then they have connected in their minds an actual customer and an actual sale that is lost.
It is different with analog cigarettes because there is true potential to harm others; but no such potential is known for personal vaporizers. People being "offended" by how it "appears" is no different than their being offended by a hat I happen to be wearing.
So I'm glad the OP sent a letter to management. By all means, be polite. But also, by all means, when nobody else can actually be harmed, I say exercise your right to vote with your feet and make a statement -- an economic statement -- that can be clearly understood.