As for the original post, 'Yes', I am choosy - because 'No', it's not my job to instill any values.
I would respond to your comment like I would several pro basketball players who got busted for crimes and then said, "I don't want to be anyone's role model."
Regardless of if you want the job or not it's yours. If you choose to do the job or not is your choice-it is still your job. Teaching is not just passing on information and techniques it is being a model of what the student should strive to be.