I'll change my answer. I actually have made up my mind.
Rose was neither selfish nor unhinged, she took a rational decision out of her situation.
After also seeing Wisecrack's revive of the themes of this movie i came to compare Finn's sacrifice to the other sacrifices which were made during the movie.
Rose must have realized that Finn's sacrifice was unlikely to be successful. For her it must have been like seeing Finn trying to rescue the rebels but realizing that if it won't work, which is much likely, she will loose Finn in vain. With no effect whatsoever. Would you let a friend run into a rolling train because you are stuck on the tracks ? I think if you could you would stop that friend.
Rose lost her sister in the first sacrifice in the movie. Right at the beginning when Poe's greed leads to a hot-headed attack on the star destroyer. Which, let's not forget, succeeds by pure luck. While nobody actually knows about the very very lucky remote catch inside the last bomber. But what everyone probably knows is that the last bomber was shot and exploding (iirc) while dropping the bombs. The attack was to 99% successful stopped by the counter attacking TIE-Fighters.
Rose following the rebellion's heroes and the stories about them must at least have known that the losses in this attack were severe ad probably realized that the result could much likely have been in vain.
Considering this in the last sacrifice: Finn's attempt to destroy the cannon it was just a logic conclusion for Rose. Poe, the guy who led the other attack on the star destroyer turns around and calls off the counter attack. Which must spark some doubt in her. In this situation Rose has enough influence to stop another dear person from disappearing from her live, much likely in vain. For her she slim chance that he might rescue everyone has far less weight than keeping someone she loves alive. Even from a non-emotional perspective, it was the most likely successful thing to do.