New Testament historians like other historians ideally should follow the historical method.
The most reliable scholarly sources (for New Testament study) come from the field of religious studies, where both the historical method and theory are used, and scholars are trained in the appropriate languages and technical skills, including opportunities for archeological fieldwork. For the field of the New Testament, the Yale religious studies program is typical:
The fundamental skills required are historical and linguistic, for the aim of New Testament studies is to understand the forms and functions of the earliest Christian writings in their historical contexts including both the culture of the Roman Empire and the varieties of Judaism within that culture and through them to understand the character, practices, and beliefs of the earliest Christian communities. At the same time, students explore various interpretive strategies, including theological, social-historical, literary, and rhetorical inquiries.
Not surprisingly, many conservative Christians do not like the findings of the secular field of religious studies. Especially since some scholars have expressly made it their mission to keep "fundamentalists in check." For example, Gerd Ludemann of the University of Gottingen in Germany, says Christian theologians follow the "dogmatic method," which secular scholars reject in favor of the historical method. And, he says it is the role of scholars like himself to keep:
Investigating and testing the text again and again, and mainly being in charge of keeping fundamentalism in check. It always wants to use the New Testament to be applied to the present, so I think that's a very positive function that a New Testament scholar can do, keeping fundamentalism in check, and all of us have the desire to get new insights, we have new sources, new discoveries for example, the Gospel of Thomas, and we want to put the New Testament in perspective, and relate the New Testament documents through these newly discovered documents, so a New Testament scholar must and will interpret the New Testament and the new insights about the environment of the New Testament to the public audience, because they want to know.
Ludemann holds that fundamentalists are teaching what Christians all used to believe before the advent of the Enlightenment with its attendant, modern scholarly methods. Their claims about the Bible simply cannot withstand the historical method. Moreover, and much like the scientists at the Institute for Creation Research, fundamentalist biblical scholars are generally prohibited from following evidence to any conclusion that does not conform to their sectarian dogma. Therefore, relying on "Bible-believing" scholars is unjustified.
Limits to scholarship
There are reasonable criticisms of religious studies experts, see the sections below which I wrote. Still other ways of studying the Bible are probably worse.
Enemies of Christianity writing embarrassing accounts
Can we be sure that only Christians were involved in telling and retelling the Gospel narrative? Opponents of Christianity might have made up embarrassing stories in an effort to discredit Christianity. When embarrassing material appears in Non-canonical gospels or in non-Christian writings generally, Christian apologists are quick to suggest these were lies told to discredit Jesus or Christianity. See Pantera for an example. There is no reason to assume lying to discredit Christianity did not also happen before the Canonical gospels were written down. Telling fact from fiction would have been difficult or impossible, especially for first century people without the scientific method. Christians could sometimes have believed and retold lies started by opponents of Christianity. Such material could easily have got into the New Testament especially if it was altered to fit Christian ideas better and discredit Christianity less.
Sociology and power politics influence consensus
Consensus over whether Jesus existed is influenced through traditions developed among researchers centuries or decades ago when Christian influence was stronger generally than it is today. Other influence happens when Christians work as New Testament historians. Further influence happens indirectly when Christians decide which research academic gets promotion, which academic or academic department gets public funding. There is disagreement whether this problem is minor or major but it can be illustrated. The section, Enemies of Christianity writing embarrassing accounts illustrates how Christians could and can influence consensus their way. Why did it take so long for anyone to notice that there is no reason to treat Canonical Gospels differently from Non-Canonical Gospels or other writings? Christians believe God supervised writings that eventually got into the Bible. Non Christians somehow followed Christian ways of thinking over Canonical Gospels.
There still is a consensus even among non-Christian historians that Jesus existed. I cannot tell if this consensus is due to the weight of evidence or due to Christian influence.
Adapted from material removed from RationalWiki