Absolutely not the case.
One does not need to engage in War during Contest of Mayors.
There are assignments that are only accomplished by participating in War, but the game easily allows a player to work around those. Many in the club I am a member of are Megalopolis League Players and none of us engage in Wars.
Yes, there are several clubs that do just fine, accumulating Legendary Chests with engaging in War.
If cheaters drive you nuts in War, why not join a Club that does not fight them and avoid the angst?
Many are out there.
Good Luck
New Goodland Mayor’s Office