Mostly the fact that a vaccination can go wrong. It's not that often but the possibility exists.
[...]
Because, if I don't want to be seen as agreeing with their whole point, I basically have to ignore this one fragment of truth.

Of course, but I'm not even ignoring this fragment. Just from stating the obivous, that infections have decreased extremely after vaccination programs were induced - which is just a fact - you get loads of angry/ignorant/denying comments. How do you find a common ground with someone that has successfully constructed his/her own seperate reality?

Not easy. Absolutely not easy.

Amen.