Religious ceremony? I'm not aware of any religious ceremony involved in transitio ad plebem, although there was a ritual involved in Clodius' adoption. Publius Clodius' transitio ad plebem was affected by his adoption (actually arrogation, since he was under his own potestas) into a plebeian family. First proposed by C. Herrenius, tribune in 59, Clodius' adoption by the plebeian P. Fonteius would have allowed him formally to renounce his patrician status. The action of adoption involved religious ceremony, but that occurred whether transitio ad plebem happened or not. Fonteius was younger than Clodius, which Cicero later argued rendered the arrogation illegal, but permission had been granted by a curiate law and was overseen by Caesar as pontifex maximus (perhaps this is what you mean?).

Transitio ad plebem, the renunciation of patrician status by an individual in order to adopt plebeian status, was not unknown, but precise references to it are hard to find. Transfer into the plebeian order by either transitio ad plebem or deminutio capitis (in which case the transfer was a punishment) must have occurred from a relatively early date, along with the transfer of family branches from patrician to plebeian status through marriage and offspring, since the fifty-some-odd patrician gentes of the early Republic were reduced to some fourteen by Caesar's time. Many of these lost branches must be from marriage, as maintaining marriages solely in the patrician order became increasingly difficult especially for down-and-out patricians (Caesar nearly married an equestrian girl when a young man, and his last two wives Pompeia and Calpurnia were both plebeians), but at least some were probably individuals undergoing transitio ad plebem, since the benefits of plebeian nobility far outweighed the few (almost all religious) privileges still enjoyed by the patrician order. References are fleeting, however. A number of very early transitiones (those, for example, of the gens Octavia, gens Junia, and gens Minucia, all of which claimed to be originally patrician before having the entire family moved to plebeian status) are of questionable nature, and Tatum brings up the possible transitio of Sulpicius Rufus, who, it is sometimes argued, transferred himself from patrician status to plebeian in order to run for the tribunate just as Clodius did a generation later, an argument which I've always found pretty unconvincing. C. Servilius Geminus (and his brother) or his father, whose gens Servilia has (to my knowledge) no attested plebeian branches before his lifetime, probably underwent transitio ad plebem somehow, as Servilius Geminus was plebeian aedile in 209 and possibly tribune earlier than that. I wish I still had access to Tatum's Patrician Tribune (I had to return it), as he lays out probably the clearest summation of the various arguments involving transitio ad plebem--if you're able to get your hands on it, check that section. Note, though, that Servilius Geminus does not appear to have been adopted, and was known for his good filial piety towards his father. Somehow he underwent transitio ad plebem without being adopted, and there are various explanations for how that would have worked. Whether there was a normal procedure for transitio that Clodius violated is not entirely clear. Cicero seems to think it is. In the de Domo Sua he argues that if patricians can undergo transitio in the way that Clodius did soon the patrician order will die out entirely, since the plebeian offices are simply too tempting, and the religious rituals and offices that must be filled by patricians would disappear. Cicero is, however, specifically talking about the violation of normal adoptive procedure, in that Clodius was adopted by a younger man and that he did not renounce any of the family rites and ties that made him a Clodian. There's a not-very-revealing comment by Zonaras that suggests that normally transitio ad plebem was not done by adoption, and that this was an innovation on Clodius' part. Tatum remarks that there can be no question that transitio was technically a process separate from adoption by a plebeian, a suggestion I find more than convincing enough but which can be disputed more than I think he cares to admit. There's a difficulty that our sources, particularly Cicero but also later authors, describe Clodius' transfer both as an arrogation and as a transitio, when reasonably the known examples of transitio do not appear to have worked this way. Tatum is probably right to say that this is just a sort of casual shorthand, but we really do not have a great deal of information about transitio

The process was more legal than religious, though it featured elements of both. In Roman law in the Late Republic, there were two types of adoption: adoptio and adrogatio. The difference between the two had to do with the status of the individual, and whether he was under the authority of a family head (pater familias). If a person was the head of his family (sui iuris), he could not be placed under the authority of another ("adopted") except via the process of adrogatio. There seems to have been precedent going back centuries into the past, but we get the impression that adrogatio was quite rare and bizarre. Cicero later complained about some technicality violations of Clodius' adrogatio, but in the main the procedure was apparently "legal" and had precedent. I can't find any specific precedent with a named individual before Clodius, however.

Here's what happened: In 59 BCE, Caesar was consul and immediately launched mischief with the help of Crassus and Pompey, his fellow triumvirs. Cicero was alarmed by this and took the opportunity, during a trial of his colleague, to attack the triumvirs and Caesar in particular. Cicero's tongue was a formidable weapon and his message hit home. The triumvirs' response was to arrange Clodius to become plebeian so that he could be tribune and act as a foil to any further attacks by Cicero. Because Clodius was sui iuris, they had to use adrogatio to get him adopted into a plebeian family as a dependent (under the potestas of another, rather than his own). They found a 20-year-old kid, Fonteius, to "adopt" Clodius (who was older).

The adrogatio required a decree of a specific type of public assembly, the comitia curiata, which was convened by Caesar in his guise as consul. Pompey, as an augur, "made sure" there were no bad omens to halt the proceedings. Caesar then put on his Pontifex Maximus hat and declared the proceedings appropriate. The assembly issued a lex curiata and the deed was done. The kid Fonteius then immediately emancipated his new adopted son, so that Clodius was again sui iuris, only now as a plebeian and eligible to be a tribune of the plebs.

Cicero later objected to this whole business, noting that Clodius was older than Fonteius, that Caesar's co-consul was "observing the skies" and therefore preventing any official business from concluding, and some other minor obscure technicalities. He was apparently alone in this, and most people seem to have accepted the adrogatio, or perhaps wisely kept their objections to themselves in face of the triumvirs and their vicious pet tribune.

For a lot more on this episode's prologue and epilogue, see Tatum's excellent book on Clodius, The Patrician Tribune: Publius Clodius Pulcher (1999).