The message
from "Ivan" contains these words:

By the use of the word 'yard' I'm guessing you're posting from USA? This
group is pretty much UK-centric though your problem isn't!

Actually, CANADA (a member of the commonwealth).

I don't know how insurance companies look at things in other countries but
here they're pretty fussy about how close tall trees are to a house and
what
damage they could do. Poplar trees are aggressive in their search for
water
so your drains and your neighbour's are in real danger of being undermined
by these trees. I suggest you have a word with your neighbour about this

We are serviced with plastic sewer lines, so there is no worry there.

It's not so much undermining that's the risk to drains/pipes, as roots
invading and blocking them, and that can happen to plastic ones. Pipes
settle over time (especially near trees). Wherever there's a join it's
possible for a small drip to leak from the seal, and where that drip
oozes out, a tiny root finer than a hair can enter. Then the root
reaches food/water and expands until it fills and blocks the pipe.
Poplars are notorious for it.

Janet.