People are vocal about what they feel passionate about, and a world where they weren't or couldn't sounds hellish to me. How would society ever progress? We'd still have "whites only" restaurants in that world.
Not saying that justifies all anger targeted at business owners, but a blanket "criticism bad" stance is a bit silly. You have to make an actual argument as to why you think the anti-AI crowd is misguided in this case.
The headline makes it sound like people are phoning in bomb threats and violence, which doesn't seem to be happening at all.
Honestly, I think the business owner should have ignored these weak "threats" altogether. It doesn't have anything to do with coffee and it's unlikely they'll get any business because they use AI, so it can only hurt them.