I knew someone would mention salt in the washing up liquid, when I was a poor apprentice still living at home my RD250 would get washed every week for two years with whatever washing up liquid I found in my mums kitchen, never did it any harm.
I think you would have to leave your bike soaking in neat washing up liquid for years for any effect to be noticed.
The leaving in on is not the problem. The fairy liquid itself is just a degreaser. The problem lies in the salt when it is rubbed over the paint. The salt is harder than the paint surface and so it causes micro abrasions and marring on the paint surface which affect the finish.
That being said, the best product in the world will do exactly the same thing when coupled with a poor wash technique. For many marring and swirls are an inevitability.
The colour of the paint has an effect as well as swirls and marring don't show up much on silver or white paint, but show up a lot on black paint.
This is a car I did a while ago which had been being washed with a poor wash method and using fairy liquid:
The sun is showing the swirls pretty clearly.
And the same car after having the swirls corrected via machine polishing:
Being honest though, most people don't even look to that sort of level and yes, it's pretty anal to the n'th degree. If swirls don't bother you then fairy liquid is no problem - it does strip wax off though so if you want your wax to last I would use something less aggressive.
I use turtle wax wash j wax from Costco - its £15 for 25 litres and does the job. Polishing I use a few things depending on what I want to do and I use collinite 476s for my waxing.