Because they're poor uncivilized savages that just go around raping and pillaging and she's their protector that will bring them into the folds of civilization. She's saving them from their barbaric ways. Damn the cost to everyone else. People think brutal savages can be redeemed because they think all people can be reformed to be civilized. They are wrong of course, but people like to dream in a utopia where that happens. So when Dany and her savages win, it's good for this weird warped point of view.
In my personal perspective of Dany, I think her story was interesting and I was going for her from the first book until she started ruling Meereen. Then when I actually looked back at how she handled everything, I realized that she was a naive young girl who doesn't know how to rule and she pisses everything she has down her leg everytime she gets power. Now she's going to burn Westeros to achieve her shitty revenge plot and everyone will suffer when she eventually pulls a Mad King like her father did.