These following two paragraphs are from one book and come one after another.
While this treatise might not appear to meet the normal requirements
of an academic paper, let it be said that such was not even our
intention. This is a work composed by a scientist and a religious
leader. If science and religion are to live side by side in mutual
non-judgment, there needs to be a new model for dialogue, one that
takes into account the interests of both sides. Religious people don't
really "do" numbers. Scientists can't get dates and don't have a
clue what real people think. By collecting and presenting a different
kind of data, we aim to appeal to "Bible thumpers" and "brainiacs"
alike. Just getting those epithets out on the table can make a
difference.In fact, we feel better already. Too many resources are being wasted
in trying to prove intelligence in all we see around us. Wouldn't it
be better just to throw in the towel, call a spade a spade, and admit
that our Creator is a dumbass?
I'm confused by the meaning of the phrase get something out on the table, and by the sentence following it as its meaning relies on the previous sentence.
Maybe getting something out on the table means calling something what it is, calling something like one sees it?
I've searched the phrase on Google Ngram which resulted in this one useful excerpt from this book.
SHG: All right, I think there is something to what you say. I mean we
might not have heard all the different perpectives that the students
expressed had you not asked them about their views on premarital sex.
And the fact that you enphasized the contrast between the boys' and
girls' view may have allowed each group to push its position more
fully.MP: So you think I was right to ask all those questions?
SHG: I think you got their views out on the table. Or did you?
MP: What do you mean?
SHG: Now that I think about it, I wonder: Did James and the other boys
really believe all those things they were saying about other boys
wanting to be satisfied and not caring who they slept with? Maybe that
was just "macho" talk. And did Colette ever explain why she thought
sex outside of marriage was "nasty"? I can't recall that she did. Even
Marcy did not tell us why she thought premarital sex was acceptable if
the partners loved each other. So maybe we really didn't get their
views out on the table.MP: Look, it seems to me that we learned a lot more about their ideas
than we would have if I hadn't asked them those questions, if we'd
just stuck to Shakespeare. Even if James was talking "macho," there
are people who feel the way he and Michael described themselves as
feeling. So it was a view that needed to come out on the table. As for
Colette and Marcy, well, maybe I should have asked them more about why
they held the views they expressed. But at least we got it started.
Best Answer
In poker, at the end of each hand, the winner "lays their cards out on the table" to show they've won. Since part of the game of poker is to try to disguise your hand from the other players, when the winning hand is laid on the table, this reveals facts that previously have been hidden or even deliberately lied about (through bluffing) by the players.
This leads to a common idiom, "lay your cards on the table" to mean showing your actual capabilities. In a negotiation, this idiom can mean revealing your actual wants and what you're willing to give in return.
The idiom is also used in a more general form, "lay [something] on the table" and with a broader meaning, to reveal things that are hidden or simply to speak plainly.
In your examples, there are people who might not normally reveal their true beliefs, and the writers are using the idiom of putting them "out on the table" to mean expressing those beliefs openly.
"On the Table" also means for something to be subject to discussion or consideration by a group. In the written example you provided, the characters views about premarital sex were "on the table". I would infer this is not a subject matter they speak often about.