A Short Response
Describing the bible as "pure" would certainly be hard to justify as a lot of it is the record of human actions and the continual failings of God's people, why would, "You shall not murder" (Exodus 20.13), be in the 10 commandments if man wasn't killing man, and doing so against God's will, thus lacking purity in both God's eyes and, I would expect, in the eyes of modern day secular opinion.
I recognise the existence of God is a controversial issue but when discussing parts of the bible or the bible in its entirety it has to be taken in the context of the appropriate author's belief in the existence of God.
The story of Lot and his daughters (not using the word "story" to imply history or myth), found in Genesis 19 verses 30-38, could never be said to be inciting or even condoning incest given that the daughters had to get their father so drunk that he didn't know he'd slept with them (verses 33 and 35). This is simply a record of what occurred (in the author's belief). I have failed to find any reference to Lot being called ""a righteous man"". The story of Lot is told in the book of Genesis, within which the word "righteous" occurs twice (NIV translation), once in Genesis 6.9, in a description of Noah, and once used by Abraham when speaking to God (Genesis 18.23).
The same goes for the story of Lot offering his daughters to the angry mob in Genesis 19 verses 1-13. For the record there is nothing to say that either of Lot's daughters were raped, let alone "repeatedly raped over and over and over again until she expired", on the contrary, the mob declined the offer of his daughters, then the two angels blinded the mob so they couldn't find the door and pulled Lot into the house, keeping Lot (and we can suppose his daughters) safe. Both of his daughters were still alive later in the chapter.
The last mention of Lot is in chapter 19 where both the stories mentioned here about him occur, so if he is referred to as being righteous in another translation it would have to have been said before he did these things.
Matthew 15.4 is not Jesus saying to kill children for cursing their parents, it is him referencing Exodus 20.12 and Exodus 21.17 to point out the hypocrisy of the Jewish teachers about a matter of ceremonial washing, as for the verses themselves it is the latter of these two verses that states the punishment, the former that sets the rule (not to curse one's parents), they are separated because the rule applies in all circumstances, whilst the punishment was meant as part of the legal system of a then nomadic tribe.
As for the matter in hand, the content of the bible being explicit, there are parts of the bible that are explicit, however people haven't been picking them out, instead they chose examples where they wish to question the morality of the bible. We wouldn't object to the daytime news mentioning that someone was on trial for rape, surely if the word "rape" can be used then the word "sex" is acceptable, which is the most explicit these stories get (Genesis 19.5). As for obscene, again, if rape and paedophilia etc. can be mentioned on the daytime news then how can we object to them being mentioned in a spiritual text?