Micro.blog seems to want to head in that direction - they're certainly on board with the chronological feed & "no likes / metrics" idea, and they have a way to import your photos from Instagram. The service itself is meant to be a social network that works via RSS:

https://help.micro.blog/2017/instagram/

But they make it really hard to even see that they have photo / Instagram-esque features, and it seems mostly connected with their iOS app Sunlit:

https://sunlit.io/

I used to be a member but found the service very hipster & Apple / iOS centric. But it might be what some people here are looking for.