The question does not ask whether biblical criticism is true, but merely how some Christians deal with biblical criticism. Most Christians are largely unaware of biblical Higher Criticism or simply choose to ignore it as being of little concern to them. Christians in this latter group is unlikely to change their strongly held faith just because some biblical traditions are being questioned.
Others look for evidence to support the Bible as they read and interpret it, and seek to undermine the conclusions of critical scholars. Sometimes, unqualified 'biblical archaeologists' have set out to use their limited skills to prove the historicity of the Battle of Jericho or the biblical Flood. As an example several 'biblical archaeologists' have visited Mount Ararat, in Turkey, and claimed to have found evidence of Noah's Ark, although in each case, no evidence was available for the general public. Some of these expeditions involved a large boat-shaped geological feature to be seen at Akyayla, a few kilometres from Mt Ararat. According to 'biblical archaeologist' Ron Wyatt, he arranged 'chemical analysis' tests of the feature that “positively prove it to be composed of very ancient wood and metal.” Ian Wilson says, in Before the Flood, page 37, the carbon percentages quoted by Wyatt fall within the normal bounds of soil and show no evidence of wood. He says that instead of the 'metal brackets' for ships' fittings, as claimed by Wyatt, the true explanation is that the Akyayla site is rich in naturally occurring manganese nodules that are high in iron. There no geological or archaeological evidence for the Flood itself, but this does not stop some Christians from claiming that professional scientists have misinterpreted the evidence.
Although the message of the Pentateuch would remain the same whether or not this was written by Moses, some Christians are adamant that Moses wrote the entire Pentateuch, including the report of his own death (Deuteronomy 34:7). For them, the proofs of multiple authorship are irrelevant, because if they learnt as children that Moses was the sole author of the Pentateuch, then this is undeniably true.
A Catholic view, expressed by Pope Leo XIII, is that the sacred writers "did not seek to penetrate the secrets of nature, but rather described and dealt with things in more or less figurative language, or in terms which were commonly used at the time and which in many instances are in daily use at this day, even by the most eminent men of science" (Proventissimus Deus, 18).