The term "active" gets thrown around here sometimes as if it described any arrangement in which a condenser microphone has its capsule connected to its body (amplifier) by a cable. But what the term really says, and really means, is that there is some active circuitry--a gain stage that is powered--in the cable (or gooseneck or rigid mounting tube or whatever else) that connects the capsule and the amplifier. Since a condenser microphone capsule has very high impedance at audio frequencies, the active circuitry is generally configured as a current amplifier, which then functions as an impedance converter that reduces the signal's impedance from very high to low.
In the 1960s and 1970s Neumann and AKG offered rigid extension tubes for their respective series of small microphones with removable, interchangeable capsules. To use them you removed the capsule from the microphone, screwed it on to the extension tube, then the extension tube screwed into the microphone body in place of the capsule. These extensions were simply shielded wires with no active circuitry in them. They were situated electrically within the ultra-high-impedance part of the microphone circuit, so their use made the microphone more vulnerable to picking up hum and RFI--and despite great care in the design and manufacture of these extension devices, there was always some degree of signal loss due to stray capacitance although this was kept to a minimum because the longest these devices ever went was maybe about two feet. In their day they were useful and even necessary in certain situations. But nowadays no manufacturer of professional microphones would think of selling a product like that, because the whole RF environment is very much harsher than it was back then.
The term "active" with reference to such accessories was introduced by Schoeps in connection with their "Colette" (CMC) series of microphones and accessories early in 1974. Dr. Schoeps and the company's chief engineer, Jörg Wuttke, who had led the actual development, were granted a German patent as well as patents in other countries (including the U.S.) for this technology.
As a result, the next manufacturer to introduce "something like that"--Neumann--had to arrange it all rather differently. Their first such product, a very nice small cardioid called the KMF 4, had its FET impedance converter built right into the housing of the capsule with a fixed-length cable attached to that. The amplifier had a socket for that cable, but no way was provided for operating the microphone with the capsule directly attached to the body. Their next iteration was the KM 100 series which is still made today, with "active capsules" rather than active cables (or goosenecks, or rigid mounting tubes). So technically, everyone who uses a Neumann KM 100-series microphone is using an "active" arrangement even when the capsule is directly attached to the body.
As for sound quality, which this thread was initially supposed to be about: No one has ever seriously claimed to hear a difference between Schoeps microphones with active accessories and without them. It's a total non-issue until/unless someone can bring real evidence that they can hear a difference, or even measure a difference of a degree that could possibly correlate with hearing a difference. And I think someone would have done so by now if they really could.
The canard about not using (solid-state) active cables with a Schoeps tube microphone (M 222) is unfortunate, and shouldn't lead to any wider conclusions. I don't pretend to speak for my friend Bernhard Vollmer (designer and manufacturer of the M 222), who can perfectly well speak for himself, but it is really a matter of the idea rather than the sound. Some people like the idea of a microphone system that has no solid-state components in the audio path at all, and this is in fact available with the M 222, unlike the "tube" microphones of some other manufacturers.
But just because Schoeps offers a way to achieve a certain idea that some people want, doesn't mean that Schoeps actually endorses the idea or even agrees that it necessarily has merit. They can be neutral on such matters, as with the CMC 6xt amplifier that has response beyond 40 kHz; its existence doesn't mean that anyone at Schoeps believes that adult humans can hear sound above 20 kHz, for which there is no evidence. Rather, it's just that they had customers who wanted this, and they were able to meet that request. They try to do that whether or not they necessarily agree with all the beliefs that a request might be based on.
--best regards