Hey I don't have cats so it might be a bit different, but I've had a few dogs over the years and I figure it would be similar. Your cats probably associate the carriers with going to the vet which it sounds like they're not a fan of. Their thought process is probably carrier = vet = no thank you.

Have you tried to put them into the carrier without actually taking them to the vet? Drop some treats in there, let them explore it at their own pace, close it for a minute or two, and then either reward or praise them after release? Keep progressing to the point that treats are no longer required to lure them and they enter on their own, but still reward them on release. Rinse and repeat (and repeat and repeat and repeat). Over time they may change their attitude towards the carrier their mindset may turn into carrier = treats and praise.

If they're not food motivated you may have to use alternate bait such as toys or nip.