I’d recommend having the landlord remove it as soon as you can. Without knowing the specific type of insulation, it’s impossible to say whether it presents a hazard to the squirrel, but my guess would be it’s not safe or, at the very least, not ideal.

The bigger issue is that squirrels aren’t very picky about where they go to the bathroom, and if its hanging out in the attic, its almost certainly relieving itself up there as well. There are several diseases that can be found in squirrel waste, including salmonellosis, leptospirosis, and others. Some of these pathogens are airborne, so you or others in the house could get sick even without contacting the waste. Additionally, if it’s up there long enough, the urine could become a source of mold.

If you’re worried your landlord might inhumanely remove the squirrel, you may be able to contact your local humane society or other small animal rescue organization that can help you capture and release the squirrel somewhere safe.

You should also see if the landlord would be willing to install mesh or screening over your attic soffits and vents to prevent other animals from finding their way up there.