Short answer: No.
I would rule they can’t, unless the pushing or pulling was part of a spell or other magical effect.
It’s a good question for 5th edition, as past editions of D&D had a distinction between incorporeal undead and corporeal undead but 5th edition doesn’t have that same distinction.
So, Shadows were, in past editions, incorporeal.
Which would mean that they couldn’t be grappled or pushed, or have any other physical attack (unless magical) put upon them.
Having said all this, there are some rules that back up my ruling within 5th edition.
Shadows are immune to the Grappled condition and given this, I would infer they cannot be physically pushed around either.
As mentioned above, the only way I would rule they could be pushed or pulled is if the pulling or pushing is from a spell or other magical source.
If it’s just the barbarian or monk trying to shove them around, then no.
This was a question ask by Aidan, one of my players, who has also started DMing. If you have a question, then please hit me up on Twitter and ask.
Over to you. What do you think and would you have ruled the same way?