Is it reasonable to ask someone to not use cuss words around you?

Assuming that it’s not in a setting where cussing would be inappropriate or expressly forbidden for all (in the workplace, in your house of worship, in a daycare, on an online forum that doesn’t allow cussing, etc), is it reasonable to ask someone to not use cuss words when around you? If you were asked that by someone, would you comply? Would it put a strain on your relationship with that person? Are you more willing to do it for certain people – for example, perhaps more for your aunt than a drinking buddy?