1. Question Restatement
Why would Christians who are circumcised be required to keep the "[Israeli] Law" - even though there is no justification through it?
2. Answer : Christian Israeli Nationals were (are) Obligated to Observe Israel's National Laws:
Circumcision, in Judaism, is called the "Brit Milah", (Wikipedia).
At that time, "Israeli Law" was essentially the same as "Religious Law" - with Roman obligations thrown in. Even though there would be no justification - before God - in keeping Israeli law, there is still a requirement to perform it, and keep the vow made. It is quite literally the "Covenant of Circumcision": a legal contract/covenant binding someone to observe the stipulations/demands of that contract - proven and evidenced by a very literal "cutting" of the flesh, (a permanent testimony).
Circumcision is a part of conversion to Judaism, and when officiated by a Rabbi, (especially today), there is a commitment to acknowledge the authority of Rabbinic Tradition, and to observe Rabbinic Halakha, (Legal Decisions). During that time, and in Scripture, it was a part of becoming a recognized "Israeli".
But even more - "Circumcision", performed religiously, is also a covenant between oneself and God - to observe the laws of the nation of Israel - given by God, and administrated by the authorities appointed over it.
You cannot simply "revoke" a "covenant"/"contract" made with God.
Once that is done, and one becomes "Israeli" - there is then an obligation to submit to the authorities. This is something that even Jesus affirmed.
All of that being said - this verse does not at all apply to the common practice of circumcising infants - outside of Judaism, without the aid of a Mohel. One could even argue that children wouldn't even be obligated under their parents' actions anyway - and can only affirm their covenant at the age of 13, (in Judaism).
3. The Context - Messianic Judaism:
I am very aware of the implications of this - especially in Messianic Jewish communities where "Christian Gentiles" convert to Judaism, (through actual Rabbi's), but still asserting a secret faith in Christianity. This is exactly what Paul is talking about.
The problem is - Christianity defines Rabbinicism as "Anti-Christ", so a Christian subjecting themselves to the approval of that authority is "dissonant" - at the very least. However, I very much believe that the majority of these people are being deceived and acting in ignorance, and Paul's judgment might not necessarily apply in these cases. For the rest, Paul is very clear: Once you have made that covenant with God - keep it. But, be prepared, because the requirements of that law are impossible to keep, but you are still required to perform it, under penalty of the law. To be able to do this, while confessing Christ is ... err ... problematic.
I interpret Jesus and Paul to be saying something very similar: "It is very difficult for a rich man to enter the Kingdom of Heaven." And then Paul, "If so, then how is it possible to be a Christian AND have Rabbinic approval?" (Both sayings pertain to someone's status and double-mindedness.)
A Christian even trying to do this, for the approval of man - is doing so in "Bad Faith", inwardly rejecting that authority, and a breach of their own faith.
Circumcision, in Judaism, is essentially the legal act of binding oneself to the laws of that nation, and then subject to all of the penalties of violating that contract. "Circumcision" was analogous to today's understanding of "Immigration" - binding one to all of the laws of that nation. Obviously, circumcision does not have the same legal affect in Israel today. But, it was certainly the understanding at that time. One cannot simply "reverse" a legal immigration.
This is essentially a "legal opinion", intended to clarify Paul's own.