Linguistically, Paul refers back to the direct object of the previous sentence - "your manner of life".
[You] (subject) let (verb)
your manner of life be worthy of the Gospel of Christ (object clause)
Breaking down the object clause,
your manner [of life] (subject) be worthy (verb)
The remainder of the first sentence further refines Paul's definition or expectation of "your manner of life" as well.
To answer Jon's question:
- "Them" apparently refers to the "opponents" in the final phrase of the first sentence.
- If we look at the larger context of the passage, Paul has made or will make the following points:
- In the process of preaching and spreading the gospel, Paul has encountered significant opposition.
- However, he considers this a victory for the gospel, for two reasons:
- It has permitted him to boldly proclaim to audiences (such as the Roman guards) that he would otherwise not have.
- With opposition focused on him, this has allowed others to spread the gospel more boldly.
- Some of the others spreading the gospel have done so for what sound like selfish, immature or sinful motives, but Paul rejoices that the gospel is spread regardless.
- Paul is uncertain whether he will be executed or released. However, regardless of the outcome he will rejoice. (Interesting side note - he seems to use the term "deliverance" to refer to either outcome.)
- Paul himself cannot decide which would be better - to "depart" and be with Christ, or to remain and continue in ministry. (I say he cannot decide - from a personal standpoint he would much rather go to be with Christ, but for the sake of his readers he recognizes that his ministry can still have a great impact.)
- If he is released, Paul would like to come visit the Philippians again.
- [Verses quoted above] Paul encourages the Philippians to continue to grow in the faith and in sanctification.
- Whether he is able to come visit them or not, he will hear of their growth.
- Specifically, he would like them to be "in one spirit" (unified), working on behalf of the spread of the gospel, and not frightened or discouraged by opposition.
- Much like Paul has been subjected to persecution and suffering for the gospel, so will his readers. In fact, they are in "the same conflict" as Paul - fighting side-by-side for the gospel. (a reference back to verse 27)
If we take it that these opponents are not saved, then the matter of their destruction seems self-evident. By rejecting the gospel, they reject its salvific work.
Conversely, he may be referring to those who are saved, but who spread the gospel through fear or jealousy toward Paul. (Verses 15-18) This could be an oblique reference to 1 Corinthians 3:10-15, in which each man's "work" is proved by fire in the end.
In either case, the contrast seems to be on the evidence found in the lives of the Philippians vs. the evidence presented from the lives of their opponents.