Mobs do not move on the carpets.
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Comments 4
If you look at MC-120599, Pokechu22's comment it says "mobs avoid pathfinding through rails to prevent stopping minecarts; this is an intentional behaviour."
MC-33359 Is about rails they are no mention of carpets at all. Like I have said this bug is in 1.13-pre2 but not in 1.12.2 and If it was a duplicate Neko would not change the Confirmation Status to confirmed.
EDIT: This bug started in Minecraft 18w22a probably because of the fix for MC-122455.
@unknown: That ticket had nothing to do with carpets. Mobs not crossing rails is intended. Mobs not walking on carpets is a bug.
Not a duplicate of MC-33359 for 2 reasons:
This report is about mobs getting stuck on carpets, not rails.
This bug is not in 1.12.2 but is in 1.13-pre2.