cats can trust and respect? I think it's a mistake to anthropomorphize animals to this degree.
I think you're doing the reverse of anthropomorphizing - assuming that because humans have an experience, then that experience must be unique to humans.
Cats have all kinds of trust signals: showing their belly to you, slowly blinking at you, circling you with tail up, fully grooming themselves where you can see them.
You won't see these signals if you don't treat the cat with respect, i.e.: invade their space without "asking" (letting them sniff your hand from a safe distance first), pick them up when their body language indicates they are just fine where they are, pet them on places that are vulnerable (belly, throat), touch their fur when your hands have lotions or other scents.