It is a false choice if one answer is discriminated against specifically. If that's OK, then persecuting religion is to be supported just by stating 'but they have a choice to change religion.'
Because you don't share a belief, does that make it OK to persecute others for it? Is their own informed view and decision about their health and how it might affect others to be over-ridden to suit yours? Is the truth 100% clear to justify yourself?
Obese people have the choice to stop eating, should we ban them from restaurants and medical services because of their 'choice?'
Fear makes people mean and willing to harm others for the sake of their own perceived risk avoidance (don't pretend it's all for the 'greater good' with all the other day to day suffering we contribute to at the cost of others) without a second thought.