Not knowing the legal landscape in Germany this point brings up one question, would there have to be someone to file the constitutional claim against the law? I believe here in the US, that is the case. The legislature could pass whatever law they want but to get to SCOTUS (and to ultimately be declared unconstitutional) someone has to actually challenge the law. Some laws are so blatently unconstitutional that some public interest group might challenge it right away. In this case, I wonder who that might be? Or is such a test automatic in Germany?
Disclaimer: I'm not German, I've only looked at the relevant wiki pages in German. And after that, I'm a bit confused how this would have to be done in this specific case. Links are to the relevant German wiki pages.
Bundesverfassungsgericht (constitutional court)
A test is certainly not automatic. Someone has to challenge the law. The German constitutional court adjudicates a number of different kind of cases (summed up in section 8 of that page), of which three seem relevant to this case.
1.
Verfassungsbeschwerde
When someone is injured in their constitutional rights, they can complain before the court. The complainant has to be personally injured in their rights. So in case the German parliament makes a law that allows religious circumcision, a five day old Jewish baby could complain before the court. Such a case, if decided in favour of the complainant, does not invalidate the law de iure, but often it does de facto.
You see the problem with this: who makes the complaint for the child? One of the parents. So only in case the parents stronlgy disagree, you'd get such a case. Legal persons can also complain under this title, but it's very unclear to me from that page if an "Association against child circumcision" would be admissible; I tend to read it as not.
ETA: This is the most popular kind of case before the court (151,000 out of 157,000), but only 3,699 were successful.
2.
Konkrete Normenkontrolle
In such a case, a lower court thinks a law goes against the constitution. It requires a concrete court case before the lower court where that law is applicable. The lower court then suspends the case and asks the constitutional court to review the law in question. So, in case parliament decides a law permitting religious circumcision, you'd need (a) a botched circumcision case, so the authorities are alerted; (b) a prosecutor who brings that case before court, and (c) a court that thinks the law is against the constitution.
3.
Abstrakte Normenkontrolle
This is the kind of case where truly a law is challenged, checked against the constitution, and stricken from the books, if successful. However, the possible complainants are quite limited:
a) the federal government (executive)
b) the government (executive) of one of the states
c) one quarter of the (federal) MPs.
In the current situation, the Chancellor, leader of the main government party CDU, has said she's in favour of such a law. The minor opposition party, the Greens, have also said they're in favour.
So the federal government is out. Which of the 17 state governments would burn their fingers on this issue? And would SPD or Left Party MPs burn their fingers on this issue by levelling a complaint? My guess is that the SPD, the main opposition party, receives a great deal of the Muslim votes, and don't want to be seen as antagonizing. Letting the courts forbid circumcision is one thing, actively opposing legislation to permit it is another thing.
ETA: Christian beat me to it and raises a good point:
Our current minister of justice, Sabine Leutheusser-Schnarrenberger, already noted that allowing special treatment, which goes against court ruling, constitution, human rights, etc., purely based on religious and/or cultural habits, will surely open up a really big and nasty can of worms. She especially mentioned FGM as well.
Yes, the junior coalition partner FDP might also grow a skin (pun intended).
ETA2: added number (2). From what I've read thus far, that seems the most likely scenario to challenge a pro-religious-circumcision law.