In Philippians 3 Paul contrast two groups. There are those who walk according to his example (τύπον) and there are those who walk as enemies of the cross of Christ (τοὺς ἐχθροὺς τοῦ σταυροῦ τοῦ Χριστοῦ). The language Paul uses is very interesting.
It is not entirely clear who these “enemies” are that Paul has in mind, but many think that he is referring to the Judaizers of 3:2 (i.e., those who mutilate their flesh, which is a pejorative way of saying circumcision). In other words, Paul’s biggest opponents were not pagans, but religious folk.
If it is the Judaizers that Paul has in mind, then two thing are worth noting. First, confidence in the flesh (i.e., circumcision, nationality and pedigree) is no different then serving ones own appetite. Second, Paul inverts the cultural narrative of his day, as he shows the contrast between glorying in the cross versus glorying in ones own shame (i.e., putting confidence in the flesh). The irony obviously being that the cross is a symbol of shame in Greco-Roman culture.
The overall point being, that if one embraces the shame of the cross (what Jesus embraced for our salvation) it is to their glory, while the one who embraces the glory of some particular culture (circumcision, food laws, etc.) it becomes ones shame. In other words, the self-generating identity that we so often seek to build through social advancement, status, intelligence, degrees, food, etc., is ultimately rubbish/poop (σκύβαλα) when compared to life in Christ.
Ultimately for Paul, the real circumcision put no confidence in flesh, but rather glory in Christ Jesus. They have a righteousness that is not gained, earned or calculated through merit (or through being culturally acceptable) but rather is gained through faith in Christ alone. In the end, the real circumcision see that it is better to suffer the loss of all things in order to gain Christ, than to gain all things and ultimately suffer without him.