It is possible to Wall Jump over the stack of anvils, but it is usually safer to wait for a bomb or the shaman to knock it down. Afterwards, avoid the bombs and be careful around the anvils. Some of them may block the hole or the cheese, but if you work together with other mice, you can push them out of the way. A known speedrun tactic is when you are on the way back, get propelled into the anvil debris by an exploding ball, but a lot of the time innocent mice get hurt from this.
Players will probably rely on you to take out the stack of anvils. The best way to do this is with a spirit, you can also place an invisible box directly under the anvils. Once the anvils are down, keep them out of the way of players with more spirits/cannonballs. Or, build a bomb shelter out of invisible boxes.
0.148 Version: The anvils now spawn in 4 rows. Also, instead of spawning balls, bombs will be spawned.