A crawler that follows links found in emails and sends POST requests / submits forms will cause so much havoc. It could buy things, validate account sign-ups, delete data, etc. I have a hard time believing the answer isn't to ask users to switch to a normal email provider.

I know web search at least runs JS to get better results. Not sure about email pre-fetch but I assume they do. I don't think crawlers click buttons though unless they are malicious so it's probably fine for unique email links.