I've served in various roles in both organizations. Here's the deal: CAP chose to exercise its prerogative under the NTIA Redbook section 5.1.3, which says, "Agencies may promulgate more stringent criteria for their own use." Consider that as there is no longer a "CAP mod." CAP doesn't want you there with anything but compatible professional land mobile/maritime/Part 90/military grade radio equipment. In many cases, CAP provides the members it wants using radio equipment with "corporately-owned" radio equipment for their use within the organization's needs.
Frankly, any radio that meets the technical specifications defined in Chapter 5 may "work." The issue was that many modified FM transceivers either failed to meet the narrowband emission mask or did not have a VCO that allowed operation on every potential frequency needed, or had a (HF) VFO function which on numerous occasions led unfamiliar individuals to go outside of the frequencies they are authorized to operate on (they have no requirement to have any radio experience or licensure other than their internal training, so consider many but not all to be "appliance" operators). CAP has also evaluated receiver performance to the Redbook standards, so that if a transceiver's transmitter materially complies, but has an overly-broad receiver, it doesn't make it into the list of vetted equipment. The Heathkit HW-18 that was in the bottom of the closet in the squadron building doesn't meet the stability or functional specifications, even though it's a channelized device.
Also, without internally required performance standards, individuals tend to insist that infrastructure equipment is defective when it's their deficient individually-owned equipment that does not function within the required environment.
Administering the compliance of an enterprise-wide radio system is extremely difficult when thousands of individual members may become wildcards.
MARS operators are required to possess an amateur radio license and tend to be (but aren't always) more familiar with their equipment. In very broad terms, a transceiver with an oven oscillator or TCXO, or GPS disciplined oscillator, with speech processing turned off, and an envelope for voice transmissions to comply with 2K80J3E (2.8 kHz bandwidth SSB) complies. Various digital modes may use a slightly greater bandwidth. Still, the organization is responsible for compliance, and there is more peer-on-peer guidance. (5.1.2 Consequences of Non-conformance with the Provisions of this Chapter - In any instance of harmful interference caused by nonconformance with the provisions of this chapter, the responsibility for eliminating the harmful interference normally shall rest with the agency operating in nonconformance.) So, VFOs are a liability, while the capability for stable, channelized operation is better-suited for both organizations. My Collins S-Line was my primary MARS radio "back in the day." It's no longer desired today. I use an Icom IC-M710 as a primary HF transceiver (it's frequency agile, but channelized) or a Kenwood TS-2000 with authorized frequencies programmed into memory, not VFO operation so I won't bump the dial with a notepad and end up somewhere I don't belong.
To be clear, the FCC has no part in either organization. They both operate under the auspices of the NTIA, with one organization requiring a valid amateur radio operator license as a prerequisite to join and maintain membership. The FCC, however, will enforce unlicensed operation when someone is not authorized to operate as a CAP communicator or is not a MARS member.
If someone is not a MARS member, or a member of the SHARES network, they don't belong there and they have no reason to "mod" their equipment. Can someone do that anyway? Sure. But, there may be consequences for misuse or abuse.