So in that population of people that distrust the news, there will be crazies that will never take the vaccine and there will be varying levels of reasonable people who decide to wait on taking the vaccine while weighing their own personal risk level with the risk of taking a quickly developed vaccine with no long term studies behind it. The longer we wait, the more of these people will decide taking the vaccine is less risky than getting covid as more studies come out, especially once the FDA promotes it from emergency approval to full authorization (which requires 6 months of data). Some of these people will of course wait longer than full authorization, they may want to wait a year or longer depending on how must they mistrust the news, its unfortunate but its going to take decades for these people to regain trust in the main stream news and the crazies I don't think will ever trust the news again.
Here's an example that used to be farther removed from today's social touchstones: Premarin. Premarin is manufactured by keeping mares continuously pregnant in stalls for the continuous collection of their urine. Should you be free to protest those methods by avoiding the product? Should a pharmacist be free to avoid stocking those products entirely if it conflicts with their ethics?
Before she passed away, my grandma boycotted premarin for those reasons. That was decades ago, before transitioning became more common. Now it's more of a hot button topic, since premarin is one of the commonly prescribed drugs for transitioning women in addition to post-menopausal women. Should a pharmacist still be allowed to avoid stocking those products?
Depending on how licensing is done, it may not be unreasonable to expect people to make the decision about whether they want to work in a profession with state requirements for service before they enter the profession.
Of course it's messier if the requirements change after they have invested the time to become licensed, but it isn't that different, they shouldn't enter the regulated profession if they want autonomy.
Individual practitioners within their field should have some level of autonomy, especially when it comes to ethics. I'm not willing to yank that away from someone just because their ethics disagree with mine. Same thing with consumers.
Some of the reasons for avoiding GMO foods are absolutely bonkers in my opinion, but I still believe in the right of consumers to make their own choices. How would the pharma landscape change if prescription drugs were obligated to carry a label that they were developed and tested with human fetal tissue or cell cultures?
(this examines the obligations and loss of autonomy more than the ethical disagreement, but there's literally no remedy for someone that believes antilock brakes are unethical, we'd tell them to pound sand. The analogy would be better if that person existed, but I think it still works okay.)