Did the ex board member actually say this exact statement?

Or are you paraphrasing and dramatising for effect?

Such an inflammatory quote should surely have a reference to be taken seriously

I've never seen anyone believe "Trans people shouldn't exist". The arguments tend to be around when and to what extent others must accept a trans person's gender identification.

No one wants to erase trans people from existence Thanos style.

I often see this hyperbolic statement ("Trans people shouldn't exist") being attached to anyone that doesn't go along with the entirety of the far-left progressive views on trans people. Most people who they attribute such a statement to are not saying "these people should not exist". There is a wide spectrum of views, most of which agree that trans people have a right to exist without threats to their person. The push back on the modern trans movement is often about nuances like whether trans women are women or a different category of their own.

I won't bother listing out the various reasons people might have to disagree with the modern trans movement. But attaching hyperbolic statements to make someone out to be genocidal is not appropriate and seems like a bad-faith rhetorical attack.

The UN human rights council has Saudi Arabia and the US on it, and they vehemently disagree on issues all the time.