Why do you think it's petty?
Personally I think it's a very big issue.
I'm not a big SM user but my DH and I follow each other on our accounts. Neither of us have anything to hide and it's never occurred to either of us that we require privacy in this regard.
In contrast I'd never consider looking at his phone or WhatsApp/Signal conversations with his friends and vice versa (even though we both know each others phone PIN in case of emergency). We respect each others privacy in respect of having a life/ friendships apart from each other.
BUT SM is different because you are sharing that content with a wide group of people rather than close friends on a private WhatsApp group for example.
A person who is prepared to "share" their life with many people on IG or other platforms but not their partner can have no other reason than that there is things they are posting they don't want the supposedly person they are closest to to see.
That's very different to being able to have private conversations with close friends.
So that means he doesn't want you to know what he's posting because it reflects a life/opinions/actions that he knows you won't like.
That's why it makes you uncomfortable - because you KNOW he his deliberately hiding an aspect of his characters from you that's he's comfortable sharing with many other people.
It's a pretty big indication of where you rank in his priorities and that's a hell of a reason to call time on a relationship when you rank below every IG contact.
Ultimately you can't truly love a person you don't know and you can't know someone who chooses to hide an aspect of their life from you while simultaneously sharing it with others.