I think it depends on how much of an ex someone is as to how inappropriate.
I don’t actually think it’s that weird to wonder what has become of someone in a casual sense, but I think it depends on how far you take that.
All my ex’s were from back in my school days. I was at boarding school though so all our relationships were pretty intense. So when you broke up you stayed friends because you had to co exist in the same space and you had the same friendship groups.
I had three fairly long-term relationships back then (as in over a year) and I am friends with two of them on social media. Because it was a long tie ago and water under the bridge.
The one I don’t know what happened to we broke up because he was a violent control freak and so I have no desire to even care where he is. But the other two, well, one got married about five years ago, and the other one is on his 4th divorce, so lucky escape there.
But I wouldn’t e.g. start messaging my ex husband, although by virtue of the fact we have children together I do know where he is in life and what he’s doing. But that relationship was different in terms of being serious/long term with far-reaching consequences.
So I do think there’s a difference.