Abundant moisture is part of the reason you are seeing moss in your beds, but a second factor is soil acidity, which is fine for strawberries, but also encourages the growth of moss.

Moss favors shade, too. Even if the strawberries are in the sun, it’s possible that the plants are providing enough low shade to promote moss growth.

There is nothing wrong with moss. You should regard it as a living ground cover. If the soil dries out for long periods of time, the moss will become dormant, so you will see it only during damp periods.

Strawberries will grow in sites that get less than full sun, but the berries won’t taste really good unless they get at least six hours a day. Your strawberries probably will develop better flavor if they get less water and more sun. Make your strawberries get by on natural rainfall unless the soil feels dry up to your big knuckle (2 inches). Give them a little nitrogen (fish emulsion) in the fall; that’s when strawberries develop latent buds for the following spring.