Dieback on rhododendron can be caused by several factors, usually centered around (or preceded by) environmental stress like drought (or under-watering) or poor drainage (or over-watering). We can't see enough detail on the stems to confirm or rule-out cicada injury, but it's a possibility since they did utilize some shrubs for egg-laying, even though they did prefer to lay eggs in tree twigs. We think we see a bit of oviposition damage on at least one stem, but you can inspect the undersides of the browned twigs for the characteristic egg-laying scar, pictured on our Cicadas page. It's also possible that cicada injury is overlapping with symptoms of another issue, so the presence of one doesn't rule the other out.

Although cicada injury might be responsible for some of the patchy stem dieback (which you can just trim off), it is not the cause of the greater degree of dieback on the plant(s) by the tree/fence. That could be due to root loss from one of several root-rotting fungi if the soil stayed wet or was watered often, or a stem infection from a fungus taking advantage of drought stress such as Botryosphaeria. Both cause foliage wilting, browning, and stem death because they deprive the branches of sufficient moisture to stay hydrated. Even once the conditions that initiated the symptoms abate, the affected stems cannot recover. Whichever of these pathogens might have been the culprit, nothing can be done except to either prune out all dead wood and hope the plant regrows from dormant buds along the stem, or to replace the entire plant. Fungicides won't be effective.

Unfortunately, what appears to be suckers ("babies") from the dying rhododendron look like Pokeweed sprouts instead. Although you might be able to cut and transplant pieces of a rhododendron stem that had rooted-in to soil it was laying on, suckers arise directly from a plant's main root system and usually do not transplant well because they do not detach with roots intact. In this case, though, Pokeweed [different link] is a very common native perennial whose seeds are dispersed by birds and other wild animals, and they can be very, very hard to remove by hand if they've established because of their substantial taproot. In cases where digging them out proves futile due to recurring sprouting, you may need to resort to spot-treatment with a systemic herbicide which will kill the roots.

Azaleas and rhododendrons are botanically closely related (all azaleas are technically in the Rhododendron genus) and do share preferred growing conditions plus have similar susceptibilities to pests and diseases. That said, what afflicted these rhodos won't necessarily bother the azaleas. Sometimes one group has a better tolerance for drought and the other a better tolerance for soil wetness, though there are exceptions and a lot of overlap in stress susceptibility, and many varieties of each are so hybridized that any tolerance differences may not matter much. Soil conditions are the most common factor when either of these plants are stressed, so make sure any roof downspout outlets empty away from their root zones and monitor the plants for watering needs during dry summer and autumn spells. The simplest way to do this is to feel the soil about five inches deep and water thoroughly when the soil feels relatively dry to the touch at that depth. Mulch is a good way to help the soil retain moisture, but try to keep it from touching the base of the stems.

You can see if any of the thicker ends of the dead branches you remove have any noticeable staining or tunneling inside, which would suggest infection or borers, respectively. Additional ailments are discussed in the page linked above, though not all cause branch death.

Miri

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