What are some environmental benefits of using a clothesline instead of an electric dryer?
Primarily the reduction of the use of electricity!
It may be one of the oldest and most reliable "solar powered" household devices! While dependent on local climate, it is inexpensive to acquire, use and maintain (and can be done indoors too).
By NOT using an electrical appliance the environment is spared a large amount of carbon dioxide emissions from the production of the electricity. Clothes driers probably are second only to air-conditioners in the amount of energy required to accomplish their function.