Two things at work here. Firstly he is a rescue dog with all that entails - insecurity, fear of abandonment, and other issues we can only guess at. With time, patience and good experiences he will become less clingy.
Secondly this breed is very much a companion dog, and his natural instinct will be to cosy up to his humans. The humans need to let him know when he can and when he can’t come up for a cuddle.
When they are eating is a definite No No, but if they invite him up for a cuddle then that’s different. I suspect Christinefrancd has hit the nail on the head and they encourage him up in their own home, and why not?
Re the cat. He (she?) is wise to hide, chihuahuas don’t tolerate other dogs or cats that well.