Using a SlutBut with the intent (intent is a critical element of entrapment and most crimes) to entrap someone is no different than chatting with the person personally, typing those chat lines manually. Using a tool changes nothing.
Disclosure IANAL
What the government actually _does_ determines whether there was entrapment, not their intent. See http://caselaw.lp.findlaw.com/scripts/getcase.pl?navby=CASE&... and http://caselaw.lp.findlaw.com/scripts/getcase.pl?navby=CASE&....
In the first case, the government assisted in a crime where the intent to break the law was clearly already present. And the judgement in the second case again makes clear that entrapment relies on there being no prior evidence of criminal intent: "If the result of the governmental activity is to "implant in the mind of an innocent person the disposition to commit the alleged offense and induce its commission . . .," Sorrells, supra, at 442, the defendant is protected by the defense of entrapment".
It would presumably come down to whether SlutBut offered illegal content, or whether it was requested of it.
I don't follow your gun analogy.
IANAL, but my understanding of the case law surrounding entrapment (in the US at least) is that the entrapped party has to have been actively induced to commit a crime. And so agreeing to sell crack when approached is not entrapment (no one was explicitly encouraged to do so), whereas repeatedly soliciting crack is.
I'm not sure where SlutBot would fall along this continuum, but it seems that there's at least a case that its use would be legally viable.