I’m wondering if there is an infection on my neighbor’s tree (scale?). I’m concerned that it’s something that could spread to my adjoining tree.
Yes, your id is spot on, that's waxy scale.
The best prevention (besides encouraging your neighbour to do some pest control) would be to make sure your plants are strong, happy and healthy, i.e. mulched, not too much nitrogen-rich fertilizer, pruned if necessary...
Should the scale decide to move over to your plot, search the site for questions tagged "scale".