Medium rare chicken is like medium rare pork. If you can get over your upbringing enough times to get used to it, you can never go back. It me took 3-4 times for each, and the only reason I stuck with it was that my snobbery overpowered my mother's education.
But really, sous-vide, medium rare chicken breast has a taste and texture you'd never think chicken breast could have. Same with pork, it's a revelation on all the things you miss out in the world due to prejudice and bad information.
EDIT: I've never gotten mushy breasts tptacek, how long are you cooking those things for? I do 1.5 hours@57-60C or so.