The advancement of public policies targeted at intangible cultural heritage (ICH) in Brazil has moved different social groups interested in receiving acknowledgment and valuation of their cultural practices and expressions. There are multiple kinds of heritage demands, related to festivities, dances, foods, languages, knowledges, and crafts, among others. Some of them express tensions and disputes around the notion of heritage itself, especially concerning the human rights that heritage implies. To exemplify the tensions and disputes that are present in the heritage field, this text addresses two ongoing demands in two major areas of mineral exploration in the Brazilian Amazon, both located in the state of Pará. The first case refers to the cultural heritage from Afro-descendant communities, self-declared as quilombolas, who are affected by the industrial mining of bauxite in the basin of the Trombetas river, in the city of Oriximiná. The second case addresses heritage demands articulated by social players related to gold digging from the basin of the Tapajós river, in the city of Itaituba and its vicinities. Both cases present significant challenges to balancing institutional practices for identification and safeguarding of ICH with ensuring human rights in Brazil, especially concerning indigenous peoples and local communities. Finally, the text argues that heritage policies should observe the proper connection between heritage and cultural rights and that the latter should be included in the broader list of human rights.