Well, the official version is of course that the illuminati only existed for about a decade before they were forbidden in Bavaria, which caused the members to say "Oh, if our order is forbidden, it must be bad and our beliefs must be all wrong. So instead of carrying on in secret, founding a kind of successor organization or going somewhere else, let's immediately stop all our actions and turn our beliefs by 180 degrees!"
Remember that there was also no mafia in the USA during the days of J. Edgar Hoover. After all such organizations would have been forbidden and Hoover even explicitely stated that there are no such organizations. Problem solved! ;)
But seriously. I think the question is leading in a wrong direction. When the order of the illuminati was forbidden in 1785, it probably stopped to exist in its historical form. But the members probably didn't change their beliefs and aims just because their order got forbidden.
Think of the US "office of strategic influence". The purpose of that government organization founded shortly after 9/11 was nothing but spreading propaganda. For example spreading black propaganda (false information, like the made-up story of iraqi soldiers killing babies in incubators) or paying influential international journalists for publishing certain "pro-american" articles.
After less than one year, the organization was closed, because it got media attention and many people didn't like the idea of their government spreading black propaganda etc.
But did that mean that the US goverment thought "People are right, the aims of that organization were bad, we really shouldn't do those things?" Of course not. The organization was officially shut down, people were satisfied, the media stopped reporting about it, but its tasks were in fact simply transferred to other organizations like the "Office of global communications" (which is a better euphemism anyway).
In my opinion, "illuminati" is just a name, discussing if an organization with that name still exist is misleading and irrelevant, and the better question would be: "what did the members of the illuminati do after their order was forbidden? For example, did they join or found organizations that might have similar aims?"