Is a Tom Collins a rare cocktail?

No, but as with many cocktails its popularity tends to wax and wane over the years.  In places like New England, its a perennial summertime favorite.

Older bartenders will know it, but younger ones probably haven't encountered it yet.  Which is kind of ironic, given that a standard bar staple is Collins Mix.  And a Collins Glass is standard glassware.

So much depends on where in the world you are, and what sort of area in town you are in.

In the mid 1960s, in a holiday job in a local tourist pub in southern England, I was asked by some Americans for 'Dry Martinis'.  I served them dry Martini vermouth, as I would to British customers. I had no idea that they were expecting a cocktail of gin and dry Martini vermouth.

These days, yes. It's out of style. Younger bartenders might never have been asked for one.

Ah, gin, lemon juice and club soda. It was Very popular back in the 1950's. But short of seeing it on a diner placemat, it would be rather rare to see someone younger than say 80 to order it. 

Not rare, but a thing of the past. I remember it from the 60s, although it was probably around sooner than that.

I'm surprised the bartender didn't google it. I've had bartenders do that for my order. 

Edit: It's from the late 1800s. The ingredients are something pretty much every bar has on hand.

https://www.allrecipes.com/recipe/222511/tom-colli...

it might be, just ask them the next time you go to the bar there