it's of course illegal¹ to tamper with the nests of species protected under the migratory bird treaty act (never encountered one though), but aside from that there's not really a hard and fast rule on this for us. since we're a conservation organization, we obviously lean towards saving the critters when we can, but it's a pretty uncommon occurrence to begin with, and more uncommon still for the critters to make themselves known before the tree comes down. most of the time we don't find out about the critters til afterward, but believe it or not, i've never seen a casualty for as long as i've been in the industry. apparently being a little guy on a tree while it's falling is safer than being a human on the ground struck by a tree.

some examples i've experienced:

• dropping one out of a pair of codominant stems; a raccoon climbed out of a cavity in the other stem and was super freaked out by the noise and vibrations, but turned out ok
• felled a single hollow tree and after it fell a family of like 5 raccoons ran out
• clearing a thicket of buckthorn that had some squirrel nests in it; moved the nests to other nearby trees and had to poke the babies back inside. dunno if mom ever found em but at least they didn't get [redacted] by the woodchipper
• speaking of the chipper, there was a mouse on a branch we were feeding into it, and when we tried to shoo it away it just ran further into the machine. then when it got to what it thought was a safe distance (not more than 18" from the cutting drum) it sat down and cleaned its whiskers. we eventually got it out by poking with another stick

my hypotheses for why we don't really run into problems with inhabited bird nests are that a. the majority of our removal phenology doesn't line up with their egg-raising phenology, b. most of our removals during baby bird season are trees that have already fallen and gotten hung up or are otherwise hazardous, which may have already shaken the birds loose, c. birds don't nest in the invasives we're targeting because they grow too densely, d. the non-invasives we remove are always in natural-urban interface areas (hence the removal) and are less appealing as habitat compared to nearby interior trees (except for barn swallows who only want to nest in the picnic shelters)

thanks for the great question, hope this answers it!

1. except between january 7 and october 4 2021 when it wasn't being enforced against incidental offenses

i saw a squirrel jump out of a falling tree today. that was cool