Individual vaccines can be argued against their own merits, but unfortunately as you say the "Overton Window" is rife with people who are swallowing down opioids like candy and believe anything that comes in the form of a pharmaceutical is gold. The reality is most medications have extensive side effects, and vaccines are no exception. Unfortunately nobody can have an honest conversation on which ones are worth it and which ones aren't because of the uneducated stigma associated with the average anti-vax beliefs.
I'd cater that the same thing is the case with climate change. I read some comments today from people who unironically believe that humanity will be wiped out within 12 years. Al Gore said that 20 years ago and here we still are.
I'd advise people to be more open minded and try and convert the anti-vaxxers to the correct side. Of course you can admit that measles isn't so bad of a disease while still promoting it's vaccines, and surely that will garner more support than advocating strapping anti-vaxxers to a table and shoving a needle in their arm.