Without going into excessive detail at this point, or derailing the discussion toward a focus on caves and away from your questions, I would suggest that what you are probably being told is that certain types of equipment may not be optimal for various environments - e.g. a Stilleto is not optimal for diving in caves. Some would state it in stronger terms. There isn't a US DOT list of 'certified' equipment for Cave Diving, or for Wreck Diving, or for Reef Diving. But, training agencies do have some minimum equipment requirements, and various instructors may have more stringent individual requirements. So, I wouldn't frame the question in terms of 'restrictions'. Rather, look at what equipment is considered appropriate for a particular environment. You won't find a lot of people diving in caves without double cylinders, back or side mounted. So, in that environment, you want a harness that will accommodate such equipment (and a Stilleto really will not). Since you have buddies who dive caves, use them as a frame of reference in considering equipment. What are they diving? If they are diving backmount doubles in caves, I would be surprised if they aren't using a backplate and wing. As for regulators, you generally won't find people diving in caves with yoke / A clamp first stages - they are using DIN. You won't find a lot of people diving standard (short) hose lengths. They are using a long hose on their primary second stage, and their alternate second stage is on a shorter hose, with a bungeed necklace. There is not a prohibition / restriction as much as a body of experience that has defined what works well and what doesn't. So, what kind of regulator configurations are your buddies diving? I am not suggesting that you build your kit exclusively on the basis of what works in caves. But, people who dive in 'serious' places have accumulated a wealth of knowledge and experience, about what constitutes safe, streamlined, high performance equipment, that can be a great guide for every recreational diver, particularly someone who might wish to ventures to shipwrecks in the future.
