This "laugh with, not laugh at" business is patently a load of cobblers which ignores a basic fact of comedy. I'm going to go so far as to say it's a stupid thing to say. Yes, stupid. A person falls down a manhole / slips on banana skin / disappears into open grave, we laugh. Jokes are about a truth revealed, often in a surprising way, and often there's a fear at the heart of the truth, which is the cause of baring of the teeth in other primates. We laugh at the person slipping on a banana skin because it speaks to us of the truth of our own fallibility. We like/need to think we are "all that", but the terrifying truth is we can be undone by a simple, stationary piece of vegetable matter.
So the reason a most -ist jokes aren't funny any more, purely on a technical basis, is that they rely on a truth which isn't the truth. For example all black people are thieves, all Chinese people look identical, all blondes are dumb, or all homosexual men have anal sex. For the joke to work everyone has to share that prejudice to start with. Thirty, forty years ago more people shared those prejudices, so the jokes worked. The comedians of the time supplied to that demand. If a joke doesn't get laughs, a comedian drops it.
It is always possible to subvert though. A great joke from Edinburgh the other year went like this: "It's so cool to be at the festival again, you get to bump into famous comedians in bars and in the street. Yesterday I was walking down Prince's Street and I saw Chris Rock, and I had to go up to him and say thanks for his N***** routine, he'd really helped to forward understanding between the races and help me sort out the issues better in my own head. But of course, it wasn't him!" Also: "What do you call a black man flying a plane? A pilot you racist cünt."
If Jim Davidson can manage to update his material like that, to match the times, then he might manage a slight comeback. I imagine he'll still be doing variations on "My mother-in-law is so fat..." which is a matter of taste really. There is a common experience of men being fearful of their mother-in-law because they don't want to watch their wife turn into that. That's enough of a shared truth to support the joke. But like I say, it's a matter of taste. As people have been pointing out, Davidson must look at Frankie Boyle, Jimmy Carr, even Micky Flanagan and wonder what's going on.
But for absolutely EVERY joke, there will be a context in which it can be funny. Perhaps the bottom line really is, "You have to laugh don't you." I think maybe it's important to be able to laugh at absolutely anything, to stave off the fear. It's proven to be good for your physical health. The BrassEye Paedogeddon Special, for example, or that satirical piece Chris Morris and Armando Iannucci did after 9/11 with a picture of the smoking towers and the headline YESSSSSSS!, or Stewart Lee's infamous "Vomiting into the gaping anus of Christ" routine.
Er, blimey, sorry, off topic and too long to bother reading.
Sexual activity has long since stopped being exclusively about procreation, so what any consenting adults do for fun is their business. In my view the people who get their knickers in a twist about what other people get up to probably need to sort their own sex life out.