Consider that if Bid’ah had such strict definitions as proposed by some, there is no way that sciences such as arts of weaponry, etc., could have been developed within the Islamic milieu, but we know this is an inaccurate portrayal, since these secondary sciences are meant to solidify Islam and its lands, so it is not a blameworthy type of Bid’ah.
(As was mentioned) Historically speaking, the scholars of Islam disputed where thinking takes place (for example discussions between Shafii’s and Hanafis). Concerning the Ahadeeth and the Qur’anic Verses in this regard, it is said that thinking is attributed to the Masdar al-Baeed (i.e. the farther source) since it is the heart that is the ultimate basis for the functioning of the brain.
In the Prophetic statement that every new thing is a Bid’ah there is an elision, its fuller explanation being that every new thing that is against the Quran, the Sunnah, ‘Ijma and Athar of the Salaf is a blameworthy Bid’ah, not just the meaning that may come to some people’s minds when reading this the first time (i.e. that absolutely anything and everything new is a Bid’ah).
Consider that even in the past, Islam often took a number of generations before it became fully established within families; thus, we should not lose heart if Muslims today are shaky and have intellectual doubts – there were many cases in the past where people fell on and off of Islam, yet today their whole family lines are Muslim.
Look into the life of Abd al-Qadir al-Jazairi (RA) and how he conducted himself against the invading French. In his life story one can find better clues as to how Jihad is to be waged practically in our times, rather than what we see many people making up today as they go along, which is a very dangerous course and harmful to the reality of Islam in so many ways.
Our Deen is basically conservative in that we do Itibaa’ not Ibtidaa’ [following, not inventing]; this is also why the modern Western academician approach to Islam is often so dangerous; since in order to gain reputation the academician must present new and original ideas about Islam even while these may have no scholarly basis in the ethos of Islam properly defined.
The Sunnis agree that any matter not of the religion is indeed a Bid’ah; however, it may be that a matter is new but has a basis in the Quran and Sunnah, so it is not technically a Bid’ah. (in here referring to evil innovations)