That is lichen and moss. Neither is an enemy of azalea, but both are opportunistic. The blueish gray lichens just need a place with the right moisture and light. The green moss actually will look for nutrients and is a sign the wood is dead or dying.

I would guess that the plant is not doing too well for other reasons. It looks like it doesn't have any mulch. It may have been planted too deep. It may have been stressed with dry, wet, heat or cold. In any case it is struggling.

It is a deciduous azalea, so new leaves should be coming out now. Any branches that don't get new leaves or have buds are probably dead and can be removed. It is best to scrape the bark to see if there is a live green layer underneath. If there is no green layer, it is dead.

Lichens growing on azaleas signal the need for better care and maintenance. Proper steps depend on individual plants but may include pruning, mulching, applying treatment for pests or fertilizing. The most important thing is drainage, mulch, and preventing drought without drowning. Only water when the soil is getting on the dry side. Most azaleas won't need watering unless they is a prolonged dry period. Next, acidic soil and proper nutrients are important. In Washington State, some soil is too acidic, so a soil test may be necessary. For fertilizer, I recommend HollyTone at half the rate on the package and only applied once around bloom time.

Here is a link that might be useful: How to care for azaleas