Only on dedicated server non-hostile creatures like beefalo, volt-goats etc. won't move while i push them during sleep.

I have a little hypothesis. Do you normally play with movement prediction enabled? If you do, try disabling it by opening the console (with the "~" key by default) and entering the following command:

ThePlayer:EnableMovementPrediction(false)

After that, attempt to push the animals again and let me know if it works.

Edited March 25, 2016 by Hypersomnia

@Hypersomnia  I even didn't know that i've been playing all that time with enabled movement prediction, tried now to disable it and push bunnyman, it works) Thank you so much Hypersomnia