While I can't speak for all of Europe nor for the late medieval, I can talk about 18th century Copenhagen and - being a little bit bold - extrapolate that if not exactly the same, the situation would at least have been reminiscent in other european cities, and probably also in earlier periods.

Executioners were not simply shunned, they were part of a special 'class' of people who were more or less social pariahs. Along with the Natmænd (Nightmen) who emptied the chamberpots and toilets of the time, and Rakkere (sometimes translated as 'Knackers') who - among other odd jobs - had the wonderful chore of taking care of dead animals, and using what could be used of the remains, they were more or less outcasts from the rest of society. Often, the executioner of the city would be only part-time and also work as a rakker - since only so many people would be executed, and it would be almost impossible to eek out a living from this alone.

Even though the work done by these three groups were highly necessary for the city, it was also the least desirable, most smelly(in an already stinking city) and often damaging to the health too. Because of this, they became almost a kind of 'untouchables' and being the son of a rakker, meant you were more or less forced to continue, since social mobility were already low and noone not already on the bottom, would hire you, take you on as apprentice, and certainly not let his children marry you! It was not unheard of, to be convicted to work as a rakker, and once you had been there, it would be nigh-impossible to get back. That said, they would often have a better life than the beggars of the city, even if the beggars were actually better 'taken care off' by the rest of the city.

My main source on this is a course I attended at the University of Copenhagen and the book, Hundermordet i Vimmelskaftet by Ulrik Langen, who also taught the course, and is one of the foremost researchers on the history of Copenhagen.

Read Joel F. Harrington's recent The Faithful Executioner. It is a nice study of one particular executioner ( who kept a journal) , mostly of Nuremberg, in the late 16th early 17th centuries. He and his family were indeed part of the underclass, shunned and kept apart from respectable citizens, though in the end he was able to successfully plead for citizenship, based on his long service.