I can't give the informed answer of someone who's tested it, but I am a chemist so can make a pretty good educated guess.
IF ANYONE KNOWS BETTER PLEASE CORRECT THE FOLLOWING.....
Ropes are made of nylon. Nylon is a polyamide. Amide bonds (wot hold the nylon together) are pretty stable under sensible conditions. However they are hydrolysed, relatively slowly, in strongly acid or alkaline conditions. Therefore I would definitely worry about a rope that had spent a lot of time in contact with either of these. Wet cement would be very bad as it is very alkaline and can penetrate - dry concrete wouldn't be an issue as it is basically rock. Cement powder - maybe less of an issue so long as everything is totally dry and it is removed very quickly but I'd still be concerned
This is also why rust marks are very bad for rope. Rust in the presence of water can create quite an acid environment, which over time will damage the rope.
In both cases the damage to the rope will be invisible. My inclination would be to cut out any section of rope that may have experienced serious chemistry of this sort 'cos rope is cheap and funerals expensive.