No espero que estén de acuerdo conmigo, pero sí que dejen de tenernos miedo.
Gabriel Boric, Presidente de Chile.
Tenernos miedo: does it mean make us afraid or, quite the opposite, be afraid of us?
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If you look in the Royal academy's dictionary for tener you will find, amongst other things.
- tr. experimentar. Tener vergüenza, miedo, hambre, calor, nervios.
So tener miedo is to experience fear and hence dejen de tenernos miedo means to stop experiencing fear of us. This also fits better with the first part of the sentence, Boric does not expect people to agree with him but he does not want them to be afraid of him.
dejar de hacer algo = to stop doing something or to no longer do something
dejar de tener miedo = to stop being afraid, to no longer be afraid
The correct parse is. dejar de = to no longer do something or stop doing something. dejar de tener miedo: to no longer be afraid or stop being afraid.
Also, you miscopied the phrase from the original: dejar de tener miedo de algo. So, the sentence says: I don't expect them to agree with me but I do expect them to no longer be afraid.
dejar de is used all the time in Spanish.
Dejé de tomar grassas. I stopped eating fatty foods.
Dejaron de jugar al tenis. Ahora hacen natación.
Dejar de tenernos miedo = dejar de tener miedo de nosotros.
To no longer be afraid of us.
In this case, it means to be afraid of us.
If it helps with understanding, consider that "tener miedo" can be constructed with "a" in some cases, not only with "de." That is, one could say something like this:
A nosotros nos tienen miedo.
Perhaps this construction makes the nature of «nos» as a sort of indirect object here more clear. Verbs that take "a" typically correspond to direct objects in English, and so when a word is included to indicate the referent of the action, it is "natural" (from a certain perspective) that it would be the indirect object pronoun «nos». Remember that Spanish indirect objects can be more flexible than in some other languages that have similar structures, English included, and so the indirect object need only receive the results of an action in a very general sense. This means that words that would be translated with various prepositions in English (and sometimes in Spanish) take indirect object pronouns in Spanish:
Le guardo rencor (I have a grudge against them/her/him).
Me robaron el coche (They/You stole the car from me)
Me va a comprar una postal (She/he/they will buy me a postcard).
Nos tienen miedo (They/You are afraid (have fear) of us
In any case, one wanted to say "make us afraid," one could instead say «pero sí que dejen de provocarnos miedo».
In English, when a pronoun is the subject of a verb, but the pronoun and verb appear in the object of a pronoun, the objective nature dominates, and the pronoun takes the objective form. In Spanish, the subjective nature tend to dominate, and the pronoun takes the subjective form. So what in English would be "desist from us having", would in Spanish (I think) be "dejen de tener nosostros". The fact that "nos" was used indicates that it is the object of "tener", not the subject.
 Note that if you translate "dejar" as "desist" rather than "stop", it better matches the practice in Spanish of following it with a preposition.