There is absolutely no way that the relationship between a domestic cat and their human caretaker can be damaged if a cat is on a lead or in a cat stroller provided the owner acts responsibly at all times.
I have done both. I’ve taken my cat out on a lead and I quite often take him out in a cat stroller. I can’t honestly say that my cat is overjoyed in being put in a cat stroller or on a lead but he warms to it. The cat stroller is very effective in getting him outside seeing new things. This stimulates the brain. When he comes home he settles right back into his normal lifestyle. There are no signs whatsoever of the relationship being damaged. If anything it enhances the relationship because I am with him more.
In fact, I don’t see how it could damage the relationship unless of course the cat is very fearful of being put into a cat stroller and finds the whole experience terrifying. If this happens and if the owner forces her cat into the stroller then that may be an experience for the cat which weakens the relationship. However, I have never heard of this happening and I don’t think it would happen. Some cats actually like being pushed around in a cat stroller.
The worst case situation would be if a cat dislikes the experience to a certain extent. Also, it’s important that the owner does not take the stroller into areas which are likely to frighten the cat but that’s common sense.
As for taking your cat out on a lead, this too can be problematic for a cat because cats are not dogs and they do not follow their owner like a dog. If you put a cat in a harness they sometimes reacts with the ‘kitten response’ which means they become floppy and silly and rollover. However, cats can be trained to walk on a lead or with a harness. In my view, it can never be that successful but, in answer to the question in the title, it does not harm the relationship.
There is one caveat and that is if a cat on a lead is walked on a journey which is terrifying for him or her and/or he becomes injured for whatever reason and the owner insists on it happening again thereafter. This may weaken the relationship between human and cat. This scenario is highly unlikely.
As for a cat feeling disrespected or humiliated under these circumstances; cats don’t, in my opinion, feel these emotions. They don’t have the emotional ability to be disrespected or humiliated and therefore the answer to that question is a firm no in my view.