Import changes contact types if you select the wrong type (ex. Organizations -> Individuals)

We found this bug after an import in a client site, but reproduced it on the demo site.

On the demo site, I created three organizations and gave them external identifiers. I then imported a csv with those external identifiers and a website value but selected "individual" rather than "organization". Instead of giving an error because the contact type was wrong Civi imported the new data and changed the contact type to Individual such that the sort name and display name also changed.