Believe it or not, parents are not encouraging their children to cry for the pleasure of annoying you. Some infants are easily soothed with a pacifier, some are not (one of mine loved her "paci", the other two weren't impressed with them). Parents w/ children are on the plane for the exact same reason you are--That is-- to get to the destination. No one, least of all the parent, likes to listen to a baby's cries. Unfortunately, all babies cry at some time. Get over it.
As an FYI on the diaper issue: The normal infant stool (especially a breastfed infant) is very loose. This is not an indication of illness. If left unattended, it stands a good chance of dribbling out of the diaper. If the mother lays a blanket on the seat, changes the baby and disposes of the wipes and diaper in the air sick bag (which should then be given to the FA)--Your health isn't being "endangered" by the diaper change.
I was a flight attendant for 5 years and saw many on board diaper changes. When I flew, only the A310 had changing tables (and only in one lav). We allowed the changes anywhere on board with the exception of the galley. Sometimes parents attempted it on the aisle floor, but this isn't usually workable as it stops all traffic for the duration. In all the time I flew, not one passenger EVER complained to me because a baby was being changed next to them. And, if they had, I would have advised them to step into the galley until the change was over if they were offended by the sight.