Prod in this context doesn't refer to one person's website for their personal project. It refers to an environment where downtime has consequences, generally one that multiple people work on and that many people rely on.
There's a middle ground here. Code for your website? Sure, whatever, I assume you're not Dell and the cost of your website being unavailable to some subset of users for a minute doesn't have 5 zeroes on the end of it. If you're writing code being used by something that matters though you better be getting that stuff reviewed because LLMs can and will make absolutely ridiculous mistakes.
It's tough to not interpret this as "I don't care about my website". Do you not check the copy? Or what if AI one-shots something that will harm your reputation in the metadata?
That sounds better. I assume the stakes are low enough that you are happy reviewing after the fact, but setting up a workflow to check the diffs before pushing to production shouldn't be too difficult
That a personal website? Prod means different things in different contexts. Even then, I'd be a bit worried about prompt injection unless you control your context closely (no web access etc).