The good news is that it's not an absolute requirement that Reggie wear a collar. In terms of microchips - the feeder I have requires collar tags, it doesn't have a microchip reader. Slowly, over weeks or months, you can work on getting him to wear his collar for longer periods of time until it's old hat and doesn't bother him anymore. If you still have his attention, put down another treat. Put the collar on him, put down a treat immediately and hope he goes for the treat before he freaks out. If you can't pair it with feeding, then just slowly work with him on it. Or if he doesn't freak out, you can leave it on him a little longer. You can take the collar off of him after he's finished eating. Hopefully he'll be more interested in eating than freaked out by the collar. Put down his food and put on his collar while he's interested in eating. E.g., prepare his feeder, walk him and his collar to a quiet place away from the others. You might even want to pair it with feeding time. If a microchip isn't an option, for whatever reason, you can desensitize your cat to the collar by putting it on him for short periods of supervised time. If he should get out, the chip will help others bring him back home to you. I agree with the others that the microchip is the best option here especially because he doesn't wear a collar. While this could take some time the goal is to get the cat used to the collar so that it doesn't react to it - last step would be slipping the collar on for short amounts of time and build up the length it's kept on until hopefully, Reggie doesn't freak out by wearing it. Eventually you can work up to putting the collar around the neck, not fastened, and of course still give plenty of treats. Keep dispensing treats as you slowly get the cat used to the collar being nearby. After a couple of days, move the collar over the cats body but not on the neck.
Last you can do try desensitizing of the collar by giving treats near the collar. Is it a break-away? Material? Are you sure it's the right fit? It also occurs to me it could be the type of collar you're using. She dislike being restricted in any way possible plus she has allergies and I'd rather she can scratch where she's itchy instead of trying to rip off a collar doing so.
But I'm sure my younger one wouldn't have liked it even if we started her wearing one when she came to us. We stopped putting them on our cats since they are both chipped and indoor only and fairly trustworthy about when we come and go in the house. Some cats really dislike collars and if they haven't worn them since they were a kitten, all the more likely. I agree using a feeder which recognizes a microchip may be the best solution here. Any thoughts on whether I should continue to try, or would that just traumatize him worse? Is this sort of thing at all normal? I certainly didn't expect him to react this badly to having a collar. I took the collar off him (he had it on for maybe 2 hours) and he's spent the whole rest of the evening hiding under a bed, albeit a different one. He went and hid under the bed for a bit and even pooped under the bed rather than come out to use the litter box. I tried again today (with the collar not quite as loose, but still I could easily fit two fingers into the collar), and while he initially seemed okay, he then started to sprint around the house and then began hiding. I'm not sure if he ever wore a collar with any of his previous owners, or if that was his first experience with one. It took me several minutes to free him as he panicked and hid. The first time I tried to put a collar on him a few days ago it was a little too loose, and he did end up in a legitimately scary situation - he managed to slip the collar under his chin, but got it caught inside his mouth. My seven-year-old cat Reggie, though, is a different story. Two of my cats are ~10 months and they took to the collars just fine - they wear them with no trouble. So I tried to get all three of my cats to wear collars so they could use an RFID-enabled smart feeder, allowing me to keep the overweight cats on a restricted diet while my other cat can continue to have free access to food as he is used to.