I like the evolution of idioms. The use of "Likewise, I'm sure" (meaning I am certain that I feel the same about it) becomes a shortened version: "likewise." I'm Canadian and this shortening of idioms is common in English cultures. It is not rude or offensive in your example. Responses such as "ditto" or "same here" or "you too" would be much more informal and more likely to be used among friends and/or family, not when you first meet someone.

It is actually informal. It's also rare here in the US. It certainly is not rude.

No, its not informal or rude at all. Replying with something like 'you too' is way more informal.