Firstly, as they say, لا مشاحة في الاصطلاح!
This term is generally used to apply to the followers of Rabi’ al-Madkhali, as well as the splinter groups thereof, including those of them who actually despise Rabi’ al-Madkhali. You might ask, how can that be?
Well, amongst the Madkhalis themselves, they use the term Haddadi for those of their own kind that they see as being extreme. The term is an attribution to a fellow named Haddad who was a member of Rabi’s circle. He took Rabi’s manhaj of jarh wa’l-ta’dil to its logical conclusions and declared that the works of ibn Hajar and al-Nawawi ought to be burned. At this point, a number of scholars stepped in and refuted him, amongst them Sh. Muqbil. Sh. Muqbil, as he has mentioned in various places, also was harsh with Rabi’ for allowing this mess, and threatened him that he should also join in taking down Haddad. Rabi did so and thus the Haddadiyyah were born.
Later, when almost the exact same scenario played out with Rabi’s former right-hand man Falih al-Harbi, Rabi took part in taking him down as well, and so the Neo-Haddadis were born. Keep in mind here that Falih al-Harbi also despises the so-called “Haddadis”, but this did not spare him from being labelled Haddadi.
In any case, those groups which have split off from Rabi’ and now despise their former cult leader, or at the least, feel lukewarm towards him, I think it is still accurate to describe them as Madkhali, as they still generally share the same worldview and mentality.
Defining Characteristics of Madkhalis
(1) Anyone who criticizes the rulers or is deemed to be doing so is labelled Khariji.
(2) Anyone who makes Takfir of secularist governments is dubbed a Takfiri.
(3) Anyone who disagrees with them or is seen to be associating with innovators/hizbis is himself an innovator/hizbi, or at the least, there are question marks concerning his “manhaj”. (note: some of them are more consistent in applying this principle than others. Rabi’, for his part, seems to be quite Machiavellian about it. He attacked some for refusing to take a position on Abul-Hasan, and defended others – namely: Abdul Malik Ramadani – because of his loyalty to Rabi)