Oh honey - you're not being overly sensitive. He's trying to diminish the hard work you have done as a parent to get your son to where he is now.
He's focusing on a VERY MINOR, extremely unimportant issue (for cripes sake, if the kid is cold let him wear his hoodie! Nobody in this country gives a flying f--- anymore if a little kid wears a hoodie in a casual restaurant - if BFs rules are that rigid things will only get worse as your son gets older.
BF refused to even consider your point that HE IS NOT THE PARENT and it is not his job to correct your child. I love that phrase - "connect not correct".
Your instincts are correct. It's not just that he was annoyed by something your child did, or had a different opinion than you about headwear in a restaurant. It's that he thinks his way is the right way and you and your son need to follow it, that he was unwilling to even discuss a different way of being with your child, and that he responded by belittling the hard work you have done on behalf of your child.
Dump him. Really. This is not you being overly sensitive.
I'm dealing a bit with this with CMM. Even though my sons are grown, two of them still live with me and both have some mental health issues (one has Asperger's, one is recovering from a heroin addiction and has severe anxiety and an eating disorder). CMM is a little rigid and also an OCD clean freak so when he comes over to cook dinner for me there is sometimes tension about what he thinks my boys should or should not be doing in the kitchen. Frankly, I'm so concerned about my youngest son and his eating disorder that I could care less if he leaves a whole sink full of dirty dishes, I'd just be happy he cooked and ate something! (Btw, my son is not that messy anyway.)
I've had to just come out and tell CMM that if he has any issue with my sons, he's to speak to me, not them, about it. That's doable since they're all adults but probably not workable with a young child and a potential live-in BF.
If you want to just keep dating him and leave your son out of your dates, then fine. But if you were hoping to progress to a live-in or marriage relationship - nope, not this guy.