@Art Maydan, I second the recommendation for blown-in (cellulose or fiberglass).

(Green board is fine under solid surface walls, from fiberglass to acrylic to whatever else, and is usually preferred, but don't do it under tile.)

If much of the basic basement finishing happened way back when, you probably have, behind the walls, plastic sheeting stretched across the concrete block walls, fiberglass batts stuffed into the rim joist cavities, organic fiberboard insulation lining the plastic, and regular drywall with untreated 2x2's serving as studs, nailed into the concrete masonry block walls with a powder-actuated nailer.

A couple of days ago a car smashed a portion of the fence, and yesterday we discovered a fiberglass shower pan is cracked so we've got completely redo the shower.

A big one-piece fiberglass enclosure?

I'd be a lot more worried about exposure to chopped fiberglass or vermiculite than mouse poo.

My tenant informed me that she slipped, fell and caused a big crack in the fiberglass tub with the knee.

Is it better to use fiberglass or rockwool insulation to insulate weight cavities before putting in replacement windows?

Home Depot and Lowes around me will give you the machine for free for 24 hours if you buy a certain number of bags of cellulose or fiberglass.

That means plumb and level and square then fiberglass hardie board.