Is 1 Corinthians 7, as it appears to be, just about marriage, and if one should marry, or is there some more esoteric meaning that I am missing? Verse 19 seems out of place.

"Circumcision is nothing, and uncircumcision is nothing, but the keeping of the commandments of God."

Anyone have some insight on this chapter to share and how verse 19 fits in here. What does this verse mean?

Moving this here for more exposure.

Verse 19 has as context verses 10-23. Paul is speaking about the person who, while living under special circumstances, gets baptized. Those special circumstances are:

1. a "brother [who] has a wife who does not believe" (v.12)
2. a "woman who has a husband who does not believe" (v.13)
3. a person "called while circumcised" (v.18)
4. a person "called while uncircumcised" (v.18)
5. a person "called while a slave" (v.21)
6. a person "called while free" (v.22)

Paul concludes that "each one [should] remain with God in that state in which he was called" (v.24). The implication is that wherever you may have been found by God is your potential field of labour for Him, an opportunity to reach others in your familiar environment and to minister to your earthly "brethren"; much as Jesus "found himself" among the Jews, so to speak, and they became his beloved brethren and people for whom He lived.

In terms of marriage then, as long as both parties can live together (in spite of one having accepted the gospel and the other not), then the Church ought not to advise divorce.

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Remember Paul is addressing a letter sent to him by some concerned members in the Corinthian church. Thus there is a sense of (they said, he said) within the letter.

It appears that the questions asked by the Corinthians were
1) Are we to abstain from relationships with our wives, or divorce in order to be accepted and better Christians.
2) Are we to be circumcised in order to be accepted as Christians.

In the first verses Paul is uplifting marriage and it's privileges as honourable, as a true commitment to the wellbeing of ones spouse. Interestingly in a society of male dominance, Paul here in verses 3 to 5 urges that women have the same rights, privileges and responsibilities as men.

In verse seven Paul mentions that it is good that for a short time a man and wife, together agree to abstain and devote themselves to prayer. This ideal is therefore, not the cessation of marriage or its privileges, but simply a short, temporary abstinence with self control.

Next Paul turns his attention to the unmarried.
He lets the unmarried know there is nothing wrong with being unmarried. He's not saying that there is something wrong with being married, rather he is saying there is nothing wrong with being unmarried either.
But natural desires urge toward marriage, and here Paul says, its better to marry than to live with constant burning desires.

He strongly urges against divorce.

So what is the main theme running through these verses including verse 19?

If you are married, stay married, don't think you need to get a divorce or ignore your partner to serve God better.

If you are single, that's great too, you don't have to get married in order to qualify for God's favor.

If you are circumcised
7:18 let him not become uncircumcised.

If you are uncircumcised
. Is any called in uncircumcision? let him not be circumcised.

In both examples (marriage and the case of circumcision) there is no need to change in order to be accepted)

Only as the Lord apportioned to each, as God has called each, let him walk.

But -- God's commandments, his moral law, that is a different thing. When it comes to God's moral law a Christian is to be transformed into a child of God.