I have tried to follow your sequence. It was not clear to me from the description if at the end you were bringing B together with C before or after they each were each in contact with A. But it turned out not to matter as either way heat will flow from C to B. If I followed you correctly, the sequences are as shown in the diagram below. The equilibrium temperatures you assigned to B and C after initial contact with A assumes they have the same mass and specific heat as A.
The thing is I don't see that your description has anything to do with the Zeroth Law of thermodynamics, which states:
If two thermodynamic systems are in thermal equilibrium with a third one, then they are in thermal equilibrium with each other.
At the end of your sequence B and C are in thermal equilibrium with each other, but neither is in thermal equilibrium with the third, A, either the original A, or the A after contact with each of B and C. Perhaps you could elaborate further at to how this applies to the title of your post.
For a detailed discussion of the Zeroth Law see
Thanks for the answer! What I meant to ask was: after the first two
steps, B and C were in thermal equilibrium with A but they were not in
equilibrium with each other. Isn't this against the 0th law?
But there is no reason why they should be. Neither B nor C were initially in thermal equilibrium with A.
To apply the law to your bodies, it would say that if B is in thermal equilibrium with (the same temperature as) A and C is in thermal equilibrium with (the same temperature as) A, then B is in thermal equilibrium with (the same temperature as) C. But that's not what you have.
Hope this helps.