What happens:
Every once in a while I find what appears to be a skeleton, but it doesn't move or respond to my presence. When I attack it, I can hit it once and it makes the hit sound followed by hearts flying, but it does not push the skeleton back. Further attacks against it do nothing, as if I am hitting air. They are unharmed by sunlight.

Most of the skeletons I find are normal, but I have found several of these bugged skeletons within several hours of gameplay. Some of the older ones I found did eventually disappear, others are still around after several game days.

Steps to reproduce:
I cannot find any way to reliably reproduce the effect, however I did perform some testing in another map and potentially eliminated some possibilities:
I spawned several skeletons from spawn eggs and tried despawning or killing them through multiple methods:
1.) moving far enough away to make them despawn immediately
2.) moving far away and letting them gradually despawn
3.) letting them burn to death in the sun
4.) killing them with a sword
5.) despawning them via distance while they are burning in the sun

I took out 1-2 dozen skeletons with each method, and failed to create a bugged skeleton.

Images:
I linked five images, of four bugged skeletons I have found thus far. There were a few more that I did not screenshot. In each image you can see that I am in survival mode yet the skeleton is clearly ignoring me, and in the sun they are not burning.

In one of the images you can see a zombie walking right through the bugged skeleton. It hesitated as if being resisted by the skeleton's push radius, but still got through and never tried to walk around. There were three zombies in a row that walked through it in this same fashion. I can walk through these bugged skeletons similarly--they offer some resistance but not like a normal living mob.