All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His Slave and Messenger.
The scholars to whom you referred in your question such as Ibn Taymiyyah, Ibn ‘Abd Al-Wahhaab, Ibn Baaz, and Ibn ‘Uthaymeen all, are honorable and venerable scholars known for their knowledge, piety, and devotion to doing good deeds. They were following the straight path in their beliefs and actions. They were students of the Hanbali School of Fiqh regarding Fiqh issues; therefore, they were indeed Hanbalis. However, whenever one of them realized a contradiction between the opinion of his school of Fiqh and the religious evidence, they would earnestly follow the religious evidence and give up the opinion of their school of Fiqh. They were not fanatical adherents to their school of Fiqh. In fact, this is the way the seeker of knowledge should be and such an attitude is not blameworthy. He is not required to be Muqallid.
As for lay Muslims, even if they belong to a certain Mathhab, they are not restricted to that Mathhab. Their Mathhab is that of whoever gives them Fatwa. They are required to ask those whom they trust their knowledge and religiosity and they should act according to the Fatwa they receive from them. Allaah, The Exalted, says (what means): {… So ask the people of the message if you do not know.}[Quran 16:43] Al-Qurtubi wrote, “A lay Muslim, who does not have adequate knowledge to practice Ijtihaad, given his lack of qualification to do that, is obliged to consult the most knowledgeable scholars of his time and country and follow their Fatwa; Allaah, The Exalted, says (what means): {… So ask the people of the message if you do not know.} He has to look for the most knowledgeable scholar until he finds the scholar upon whose knowledge most people agree.”
We would like to advise our brothers from Ahl Al-Hadeeth to call their Muslim brothers to Allaah kindly, leniently, and wisely given the prevalence of ignorance. Allaah, The Exalted, says (what means): {Invite to the way of your Lord with wisdom and good instruction, and argue with them in a way that is best. Indeed, your Lord is most knowing of who has strayed from His way, and He is most knowing of who is [rightly] guided.}[Quran 16:125] ‘Aa’ishah reported that the Prophet said: “Allaah is Forbearing and He loves forbearance, and gives reward for forbearance as He does not give for violence, and as He does not reward for anything besides it (forbearance).” [Muslim]
Allaah knows best.