What if I quit an alliance, what would be the consequences?

When you quit you wont have access to the alliance store, you wont be able to attack wendell the clown or make other rally attacks. You won't be able to claim the alliance rewards in clash of zones. If you are in a doomsday event you will lose access to your honor buildings. And if there is conflict in your state you wont have any backup / protection from your alliance members.

You can of course immediately join another alliance once you quit one. If you want to move alliances that is what you have to do first.