The bug
Some mobs strafe on certain blocks they move extremely fast (1.5 times as fast as hostile endermen), and move straight toward you instead of strafing. Just hit a skeleton in third person in Survival to reproduce, or let it walk on certain blocks like rails, they will go berserk!
Also noticed that if you run down a hill with a horse, the skeleton will "hover" or "slide" towards you.
Affected mobs
Skeleton
Illusioner
Piglin with crossbow
Affected blocks
air
chests
daylight sensors
enchanting tables
end portal frames
grass paths
farmland
lava
water
magma blocks
honey blocks
rails
slabs
soul sand
Linked issues
is duplicated by
relates to
Attachments
Comments
Could you make a list of affected blocks?
Confirmed for farmland.
i can confirm this with grass paths, chests, slabs, magma blocks, enchanting tables, end portal frames, water, lava, and air causing agility bugs when falling or hurt which means that hitting a skeleton also causes glitches. I will edit my report on this bug. I created a new ticket that is related to this one, MC-105588
I have also confirmed this with illusioners.

Confirmed for Daylight Sensors

confirmed for soul sand
This is probably because of the AI of entities on non-solid blocks. They likely have a pathfinding glitch and want to get to the nearest solid block, but being on a non-integer Y level confuses the pathfinding. This happens with passive mobs as well, and they end up spinning is circles on top of fence blocks. This sort of bug has been in the game for a long time.

Here is a video that clearly shows the skeleton running straight at the player when on soul sand and iron trapdoors.
Edit: Confirmed in 17w43a.
I think Jeb should reduce the speed of skeletons, and reduce the difficulty of the game
confirmed for slabs
This is also confirmed for 18w19a because the skeletons (that now sink) will still swim unusually fast, which also makes this bug more noticeable.

Confirmed for 1.14.2 Pre-Release 2
Confirmed for 1.14.2
Confirmed for 1.14.4
Also it happens on the block "farmland" aswell
Skeletons swim at the same speed as the player when in water so that's intended.
@Greg Milson This was never intended. Skeletons should strafe when in water which is not happening.

Still happens in 1.15.1 ... died on skyblock (built in bottom slabs) due to a skeleton going crazy. This seems to happen on any non full block, e.g. when the skeleton is not at perfectly rounded Y coordinate
Confirmed in 1.15.1, slime blocks are also affected. Video
Confirmed 1.15.2
Confirmed for soul sand. This glitch could be a serious problem in the soul sand valley, as skeletons frequently spawn there.
Confirmed for piglins with crossbows.
Still happens in 20w09a.
This was fixed in 20w11a. The skeletons no longer have the speed issue, however, they still don't strafe on certain blocks. I made a report on the behavior without the super speed: MC-174500
this ticket is duplicated by MC-100588