I think you're thinking of the cult of Magna Mater, but you seem to be confused about some things. First of all, the cult of Magna Mater, or Cybele, was not a Roman cult, it was a foreign cult introduced from by the Pergamenes from the vicinity of Mt Ida in 204 at the request of the Sibylline Books. While Magna Mater was not generally distinguished from the Phrygian goddess Cybele the Romans were distinctly aware of her foreignness, even if she was very much an acceptable foreign cult--she's often called Phrygia or Idaea or something of that nature because of it. Second of all, Cybele/Magna Mater was not only a fertility goddess, but a sort of general protectress--she protected against disease, gave prophecy, and within the city she wore a mural crown that protected the city at war (c.f. Tyche). Finally, castration was not nearly as common within the cult of Magna Mater as Catullus 63 would have us believe. In point of fact, ritual castration only appears in the city beginning in the 2nd Century, B.C., well after the establishment of the cult in the city, and it was never a particularly major part of Cybele's cult as it existed within the city.

The cult of Magna Mater was never considered for a ban (she was, after all, sanctioned by the Sibylline Books), but it was heavily regulated, particularly because elements of the cult were peculiarly foreign to Roman ritual. Magna Mater was not in fact a very prominent cult, even if technically she was extremely important. Her cult was limited to her Palatine temple and was more or less a foreign cult transplanted wholesale to the city--her priests were all foreigners, brought from Asia Minor, as Roman citizens could not legally hold the priesthood of Cybele (though she was overseen by the quindecimviri sacris faciundis) and Italians seem to be only rarely affiliated with the cult. Under Claudius the position of archigallus, a (uncastrated) Roman citizen who oversaw the Galli, was introduced, but by and large Magna Mater remained a rather isolated goddess. She only had a handful of public festivals, the most important of which, the ludi Megalenses in April, was celebrated by the aediles and urban praetor and consisted of a ritual procession and a purification bath, with little involvement by the actual priesthood of Cybele, although they were there. Her other major festival, in March, was more centered on Attis than on the goddess herself, and it's really only this festival that involved the priesthood and Cybele's other hangers-on.

The Galli, which is what you're interested in, were really not that big a part of Cybele' cult, although to a Roman they were perhaps the most notable, being so bizarre to them. The self-castration of the Galli has absolutely nothing to do with preference of femininity over masculinity and it's patently absurd to connect it to dodging military service, as Roman citizens were barred from self-castration of any kind, with the total loss of citizen's rights. The Galli were one of the Μητραγύρται, the wandering beggars of Cybele. They were neither priests nor initiates into Cybele's mysteries, but rather itinerant beggars who sought alms for the goddess. The Galli and other Μητραγύρται at Rome were only allowed out of Magna Mater's temple on particular days, most important of which was her festival in April, which commemorated the castration, death, and then resurrection of Attis. In particular on March 24 the Galli could probably be seen ecstatically dancing to the sound of tambourines (an instrument closely connected with such ecstatic cults), pipes, and cymbals (often closely connected with the Galli) in front of the cult statue during the procession in honor of Attis. The Galli and the Μητραγύρται thought of themselves as slaves of the goddess, and the self-castration was the culmination of an ecstatic frenzy--with it came a sort of transitional state, both between male and female and between worldly and spiritual, as the Gallus rejected his worldly self to give himself entirely as the object of the goddess. The Galli were also generally not random schmucks watching the procession of Cybele, they were usually already adherents of the goddess and members of her procession--Lucretius describes the procession of the Magna Mater as being preceded by a train of Μητραγύρται and other attendants, who worked themselves up into a frenzied state and castrated themselves in ecstatic revelry. These aren't just people watching on the streets who decide that that looks like a swell idea, drop their pants, and yoink themselves, the self-castration of the Galli was the culmination of a very long and involved process of devotion to the goddess, and the act of self-castration itsel

But as I said, this is not an initiation ceremony, strictly speaking. The Galli were not initiates into the mysteries of the Magna Mater, nor were they priests--once again we see their sort of transitional status, where they're caught inbetween worlds. The Magna Mater had her own mystery cult and initiation ceremony, involving the taurobolium, a bull-sacrifice whose details we're uncertain about, but which doesn't seem too unlike the Eleusinian initiation.

I'm not sure where you're getting the idea of diminishing manpower and dodging military service from though. Roman citizens couldn't become Galli and we don't really hear of them doing it illegally either. Nor were the Galli an especially large group, they were an extremely small part not only of Roman cultic life in general but even of the cult of the Magna Mater, which included all sorts of attendants (none of the rest of whom were castrates), including several entire collegia, cutators and other administrators, male and female musicians, etc.