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".
I think you'll find that scale insects are often plant, or plant group specific, so unless there's a suitable host in your garden you shouldn't have a problem.
However, talk to your neighbour, and of course you have the right to prune any branches that cross to your side of the fence.