I posted an article on this topic on my blog.
The nowadays offspring of Ahlul Bayt belong to either Ahlus Sunnah, or one of the Shia groups. While Ahlul Bayt in the early days had their own Math'hab, and it was not entirely documented due to the consistent persecution and murder they were subjigated to, but many of them specifically after the 5th century of Hijra went to follow either one of the Sunni Math'habs or one of the Shi'i Math'hab, depending on their circumstances and the area they lived in.
Furthermore, most if not almost all (not all, but almost) the Ulema from Ahlul Bayt in nowdays world are not really on the footsteps of their ancestors, due to the obvious disconnection in knowledge, but instead they learned from the other schools of Fiqh/Aqidah, and adopted them.
Therefore, in reality, they represent Ahlul Bayt in their genetics only, not in their ways and methods, and knowledge. The reason behind this is because most have learned their knowledge from outsiders of Ahlul Bayt, and rarely, will you a continued line of knowledge (not geneology) through Ahlul Bayt all the way among Ahlul Bayt scholars nowadays.
That applies to both camps. The 12'er Shia camp has its math'hab entirely founded, written, and documented by non-ahlul bayt, despite their wide claims of being the "math'hab of Ahlul Bayt". That is just words, and their scholars know the reality. The founders of their Math'hab were those who were lovers and at times extremely narrow minded to the people among Ahlul Bayt they knew. Ignorant of the rest, etc..
Hence, in that respect, schools such as Imam Abu Hanifah and Imam Shaf'i specifically, are much closer to Ahlul bayt than the 12'ers. I mean the Imams themselves and their opinions, not necessarily a recent Shafi' scholar or a recent Hanafi' Scholar.
Therefore, do not be amazed if you see among "Ahlul Bayt" scholar nowadays who is a Nasibi because his knowledge was never recieved from Ahlul Bayt in an unbroken chain to the teaching of Imams like Ja'far, Musa, Al-Husayn, Zayd, Al-Hasan, etc..
Most of their teachings ( even if has a little long chain) but it stops somewhere, and says he follows such and such. With -of course- all due respect, but you have to remember that during the first 3-4th century of Hijra you could never find anyone from Ahlul Bayt who followed any Math'hab other than the Math'hab of the leaders of Ahlul Bayt at his time.
( Of course with all due respect to other Math'habs), but Imam Abu Hanifah came to learn from Imam Sadiq, and the children of Imam Sadiq learned from their father, they didn't need to go to anybody else.
That knowledge stayed in them, until most were killed, jailed, etc..and people went to the honorable students of Ahlul Bayt, such as Imam Abu Hanifah and Imam Shafi'i.
Yet, a minority of them kept lots of what it could hold from the teachings of their ancestors, and a few remained.
Hence, Shi'a in the sence of 12'ers is a new Math'hab, and Sunnism is also a Math'hab. All claim to have taken from Ahlul Bayt. Unlike what the 12'ers claim, there is no exclusivity for them. Except we- Ahlus Sunnah- are closer than the 12'ers to the teachings of Ahlul Bayt.
The reason we did not get the name for that, is the presence of the Nasibi's amongst us under the name of Ahlus Sunnah.
But, if one examines the situation carefully, you would see that Nasibi's (despite their claims to be hanafi's, shafi'is, Ash'ari's, Maturidi's) are not truely Sunni's, because they lack the most important pillar of sunnism after tawheed, which is the stand from Ahlul Bayt.
Those are some facts that most people do not know, or don't see. Hence the massive confusion.
Finally, while Nasibi's means the enemies of Ahlul Bayt. Remember it is never apparent nor obvious, as becoming an obvious enemy to Ahlul Bayt automatically means Nifaaq, etc.
Hence, Nasibi's have always claimed since their Master Yazid bin Muawiyah and on his tongue that they are lovers of Ahlul Bayt. Of course, they did everything to stop them and stab them in the back.
Today, the spiritual offspring of Yazid bin Muawiyah continues in the very same hidden ways, but you can easily identify them through two tools:
1- Supression of the events, Seerah, struggle, martyrdom, objectives of Ahlul Bayt. ( Most don't even know it to start with).
2- Glorification of the enemies of Ahlul Bayt, i.e. those who fought them, killed them, hurt them, gave them hardships, etc..and finding excuses for those tyrannts.
Finally, going back to the other big problem which is those who claim to be from Ahlul Bayt, but are Nasibi's. That goes back to them learning on the hands of Yazidi's, and the biggest sign is that they are completely ignorant in the Seerah and struggle of Ahlul Bayt. Furthermore, Ahlul Bayt are rarely mentioned on their tongues.
While we love them and respect them naturally, but they surely dont represent the ways of Ahlul Bayt.