Remember, they are also very, very, very stupid and bad at math.
Accept the fact that any vaccine, like MMR, has a certain percentage chance of bad outcomes. Seriously, everything good for you has some sort of risk - broccoli is a superfood, but I guarantee you that there are a handful of people out there who are deathly allergic to it.
Then accept the additional mathematical fact that a disease like measles has a certain fatality/serious/long-term complications rate.
Which one of those numbers is HIGHER? That should drive your decision. I've used the analogy repeatedly here, but it holds true: these fucking idiots are the kind of people who refuse to wear a seatbelt because "seatbelts trap you in the car, and when it goes over a bridge into water or bursts into flame, being trapped kills you"....which is indeed true in some situations. There are cases where wearing a seatbelt actually CAUSES a death. The problem is....those handful of cases are vastly outweighed by all the times that wearing a seatbelt SAVES someone from death or serious injury. In 1 in 10,000 wrecks, a seatbelt causes a bad outcome. But in 1 in 10 wrecks, seatbelts save lives/prevent serious injury. Vaccine refusal is for people who are stupid bad at math.