I raise arabians, and they tend to be more prone to club feet than other breeds. I had two horses at one time that both had club feet. It was not severe in either horse, just a slight difference in the angle and size of one of their front feet.
Neither had to have corrective shoeing, and neither took a lame step during the time I owend them. One was a hunter horse and the other a reiner. Both were worked hard and did fine bare foot with proper trimming. Our farrier trimmed their clubbed feet a bit differently than the other hooves, but like I said, they never needed shoes.
I think it depends on the extent to which the foot is abnormal. If it is a severe club foot and it obviously affects the horse's gait, or causes him pain and jumping aggravates it, then its probably not a good idea. However, I have never seen a horse with a hoof that is clubbed so severely that corrective trimming/shoeing (or in the worst cases, surgery) can't fix the problem and make him/her ridable. And in most cases, completely able to compete in athletically challenging situations.
In other words, I agree with you. People who say you are being mean just because you are riding a horse with a clubbed foot are ignorant. If the horse isn't in pain because of it, then you are not wrong to do so. Your horse's stiffness is most likely due to something else entirely. Particularly if its a stiffness experienced through his whole body. His age, the condition of his joints, and the fact that jumping involves allot of concussion are probably more likely to be the factors involved in making him stiff. My club footed horses competed well and were happy, pain free individuals.