And Jesus, which is called Justus, who are of the circumcision (περιτομή). These only are my fellowworkers unto the kingdom of God, which have been a comfort unto me. (Colossians 4:11) 1
For there are many unruly and vain talkers and deceivers, specially they of the circumcision (περιτομή) (Titus 1:10)
First, by way of analogy, consider the word γυνή which is translated as either either woman or wife. A single word may have two different meanings. The translator chooses one by the context, which in some cases may be ambiguous:
Another parable spake he unto them; The kingdom of heaven is like unto leaven, which a woman (γυνή) took, and hid in three measures of meal, till the whole was leavened. (Matthew 13:33)
Was it a woman or a wife who hid the leaven? The text and the context support either one. The only certainty in the parable is that the one who hid the leaven can be identified by the physical characteristics shared by γυνή. Perhaps the best "translation" would be to preserve the original word and require the English reader to learn the meaning of the Greek.
In the context of this question, γυνή are known by natural physical conditions from birth while περιτομή are known by unnatural physical conditions performed after birth. In other words, all γυνή were born that way while all περιτομή were made that way. Under the Law, a male was made a περιτομή shortly after birth at the age of eight days. The περιτομή was a decision made by the parents and one in which the male was not consulted or given the opportunity to consent. Effectively, both γυνή and περιτομή are God's workmanship, one by action within the womb; the other by parental obedience to God's covenant with Abraham and/or the Law given to Moses.
The physical characteristics of either γυνή or περιτομή say nothing about their current physical standing within their community. That is, the outward appearance of γυνή will only confirm she is female; it reveals nothing about her marital status, which must be ascertained by other means. Likewise the outward appearance of περιτομή reveals nothing about their belief in God, Jesus, or anything else for that matter. In almost all cases it is a physical characteristic that indicates what some else did and believes. 2
The περιτομή must be queried on the significance they currently attach to their physical condition. More relevant to the OP's question is the significance others place on περιτομή. Just as a γυνή could be shunned for either her appearance as a woman or behavior as a wife, the περιτομή could be accepted or not based on their behavior. The significance of περιτομή both individually and to others within any community are independent of the physical condition and must always be found with the context of the passage.
In the same letter, Paul states there is no significance to circumcision for those in Christ:
Where there is neither Greek nor Jew, circumcision (περιτομή) nor uncircumcision (ἀκροβυστία), Barbarian, Scythian, bond nor free: but Christ is all, and in all. (Colossians 3:11)
Finally, there is additional significance to the specific reference Paul makes in the letter to Titus:
But neither Titus, who was with me, being a Greek, was compelled to be circumcised (Gal 2:3)
Titus who was not περιτομή was not compelled to be περιτομή yet he was accepted by some περιτομή and (apparently) rejected by some περιτομή. So in the personal letter Paul can be seen as reminding Titus of what has already transpired and his acceptance among the leaders of the church in Jerusalem despite his not being περιτομή.
1. King James Version
2. Ignoring the unlikely event of self περιτομή. Also Scripture does have instances where περιτομή was done as an adult, but once healed the man περιτομή at birth or as an adult have the same condition. Their current beliefs about περιτομή are still a separate matter.