What’s the right adjective or noun for someone who does not trust the intelligence of another person?

good sport

someone who can accept a loss in a competition or can accept being the butt of a joke.

It is used as a noun. The definition is related to being able to take a joke but it also covers accepting criticism with grace.

As an adjective, I would say easygoing. This would describe the type of person.

relaxed in manner or attitude; inclined to be excessively tolerant

As a phrase, there is have a broad back:

not be easily hurt by criticism

It helps to have a broad back in showbusiness.

But this goes back to thick-skinned:

not easily hurt by criticism, insult, etc.

As you said, thick-skinned has two meanings. One of the meaning is what you ask but the other one is what you want to avoid. It would depend on the context then.

A tease.

1. a person who likes to play tricks and jokes on other people, especially by telling them something that is not true or by not telling them something that they want to know _{(Oxford ALD)}

Beware of sense 3, though.