And Hitler himself was a big believer in no smoking spaces. That doesn't mean that anti-smoking groups have anything to do with the genocide Nazis engaged in, just because Nazis were also officially against smoking.
Person A believes thing 1.
Person A believes thing 2.
Therefore people who believe 1 also believe 2.
This line of reasoning can be rhetorically powerful but it's flawed and, IMO, toxic to the discussion.What I actually said was:
People in set A believe thing 1.
People in set B believe thing 2.
There is a strong overlap between set A and set B.
You'll note there's nothing about a causal connection, only a correlation.[edit for formatting]