Most likely, in all these cases the story would be posted anyway and then some small minority of users who find it offensive would flag-kill it. If the moderators/vouchers disagree, the story and comments might be resurrected. Which is to say, things would work much as they do now.
The difference would be that there would be at least one day per month when unpopular opinions could be voiced without (potentially) being censored. The most important unpopular stories of the previous month would get some discussion, whereas currently they get none.