What really matters here is that he's completely shutting down the conversation, and that's more worrying than the likes themselves. Three years together means you should already be able to talk about things that make you uncomfortable without him closing the door on you. The fact that he gets upset and says "it's in the past" is just a way of not resolving anything, just sweeping it under the rug.
Try approaching this from your emotional perspective instead of focusing on what he's doing: "Look, I don't care if you follow them, but it makes me uncomfortable that you won't even talk about why. I need to understand what keeping that contact means to you, because I also have the right to feel secure." That's different from accusing him of emotional infidelity or something like that. What you're asking for is communication, not for him to delete his exes from the internet.
If after explaining it like that he still refuses to talk, then you've got a real problem. Not because he's liking Instagram posts, but because in a three-year relationship he should care that you feel okay. People who refuse to explain their actions often don't want to change anything either, and that's a real red flag.