Dish soaps are actually fairly harsh detergents and will do a great job cleaning pots and pans with baked on grease - they'll strip wax, no doubt about it. Compared to a good quality car wash soap they are very harsh. But is that a bad thing? Well, for the odd wash or two before a complete detail, no. For regular use, maybe. If you're to wax after washing, and dress all the vinyl and rubber seals, then it's probably not a big deal. But the problems are when the average guy on the street uses dish soap all the time, and only waxes his car the first month he buys it, then never again in 6 years. Dress the vinyl and rubber? Nope, he'll never do that. And he'll end up with badly faded black plastic trim and wonder what the heck happened.
But even though it's safe if used from time to time, do you ever REALLY need to use it? Like before a full on detail session? Claying will take off your wax, so will a paint cleaner. Are you going to machine polish to get rid of some swirls? Think you can effectively remove the swirls and still leave your wax on the finish? Of course not. So even then, you don't HAVE to use a dish soap to strip the wax.
Funny thing is, some people worry about a "wax build up", while others believe they're "layering". So, which is it?
Best bet, just stay away from the dish soap and stick to a good quality car wash soap. Best practices is always the way to go.