I will never understand, how one can seriously ask, if Sharia law should be tolerated in the Western world. No! Of course not. When you move to a new country, the rules of that country apply. You don’t like it? Consider migrating somewhere else.
Culture? How nice for you! When it concerns food, dance, musical preferences, the way you decorate your house etc. But “honour” killings are serious crimes according our law. And please, this is not “honour”. A woman who does not live her entire life exactly the way you want? That has nothing to do with honour.
It is insane to even have the discussion of “should we allow it?” here, as “it is their culture”. Insane. These agressors should be not just prosecuted for the crimes they commit, but it should be interpretated as a hate crime as well. According to our law, the murder of somebody because of their religion and/or sexe: it is a hate crime.