Learn English – How to use the expression “throw oneself into something”

As this ELU answer indicates, the correct version of this phrasal verb is actually to home in (to head directly towards a target). But OP shouldn't let that bother him; quite possibly most native speakers use the "wrong" version.

So the combination isn't really in + on - it's home in + on. It occurs with other phrasal verbs of the general type [verb] in, such as...

I'll look in on you this afternoon (to look in = visit briefly)
We'll check in in the afternoon (to check in = confirm arrival - at a hotel, for instance)
The burglar broke in in the night (to break in = enter illegally by breaking a lock or window, etc.)

As those last two examples show, although it might look a little odd to some, there's nothing "incorrect" about repeating even the same preposition. The first occurence is part of the phrasal verb, the second is just a normal preposition indicating the relationship between verb and object.

EDIT: Per comments below, I've just changed "sound a little odd" to "look a little odd" in the above text. The stress patterns of normal speech mean you'd barely notice the same preposition occurring twice (one would normally stressed, the other not, so they'd sound very different). But in the written form it's distracting/off-putting for the reader. Suppose, as per @J.R.'s example, your first thought was to write...

I didn't understand what she was getting at at first.

In that particular case, you could just insert a comma between the two at's to help the reader along, but it's only a partial solution which won't always work. Unless you're committed to accurately reporting actual speech, a little rewording is probably better...

At first I didn't understand what she was getting at.

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.