Brazilian groups tell why they opposed the concordat
An alliance of anthropologists, gays, teachers, judges, as well as atheist, Protestant, pro-choice Catholic and Afro-Brazilian religious groups urged Congress in 2009 not to ratify the concordat. They protested that it violates the constitutional separation of church and state and also goes against the values of Brazil which support diversity. Here are translations of some of their statements.
Among the opponents of the concordat  was the Brazilian Association of Umbanda Temples. Umbanda, like Candomblé, is an Afro-Brazilian religion that blends African religions with Catholicism. As a minority religion it feared renewed pressure from the Catholic Church. In this joyous video a prominent Umbanda, Clara Nunes sings in an Afro-Brazilian shrine, where we see the cowrie shells used for divination, as they are among the Yoruba. The song is about the purifying bath with basil practiced in Umbanda to remove the evil eye, with additional help from amulets and Catholic saints. 
The Catholic church, with its legions of lawyers, has no trouble taking full advantage of concordat privileges like recognition as a legal entity, the allocation of land and tax exemption (articles 3, 14 and 15), but this is not always the case with Afro-Brazilian religions like Candomblé. 
Criticism of the concordat was also widespread among Protestant groups, at least initially. Opposition was voiced by the Gospel TV programme, Victory in Christ by the evangelist Silas Malafaia, and two interdenominational organisations, the Council of Pastors of Brazil (CPB) and International Council of Protestant Ministers of Brazil (CIMEB). These combined to publish an open letter to the nation in the main newspapers.
However, the opposition of Malafaia and many others changed to support for the concordat when they were offered a semi-concordat of their own, the “General Law on Religion” (Lei geral das religiões) which lets them proselytise in the schools.
The Brazilian government is making an agreement with the Catholic Church
to the detriment of all other religions
Association Victory in Christ / CIMEB - Council of Pastors of Brazil, 25 August 2009
[...] This agreement benefits the Catholic Church through the evangelization of the Brazilian people in various sectors of society, including hospitals, schools and armed forces.
The most serious [objection] is that this agreement is contrary to article 19.1 of the Brazilian Constitution , which says:
The Union, the States, the Federal District and the municipalities are forbidden to:
I — establish religious cults or churches, subsidise them, hamper their operation or maintain with them or their representatives relations of dependency or alliance, with the exception of cooperation for the public interest, as set forth in the law. [...]
III — create distinctions between Brazilians or preferences favouring some.
Our nation can not enter into alliance with any religious group which violates the principle of secularism, and also promotes the breakdown of national equality!
Approximately 70 million Brazilians who are not Catholics are being discriminated against. We are convinced that the majority of Catholic people do not agree with this absurd grandiosity because they are democratic people.
With the approval of this agreement the Holy See will be fully able to reach agreements with the Brazilian government through Catholic Bishops CNBB, without ever having to go through Congress.
[Article 18.1 of the concordat says:
“Departments of the Brazilian Government within their powers and the National Conference of Brazilian Bishops, duly authorised by the Holy See, may conclude agreements on specific issues to implement this Agreement.”]
This is a real “blank cheque” for the Catholic Church. This is a disgrace! [...] For the sake of the secular state, SAY NO TO [THE CONCORDAT].
Declaration of the Methodist Church about the Agreement between the Vatican and Brazil
Igreja Metodista, 4 March 2009 (excerpt)
See also the interview with Roseli Fischmann:
a) We reaffirm the right of religious freedom as one of the indispensable pillars of a democratic society and, accordingly, one of the crucial achievements of Brazilian democracy.
b) We proclaim the constitutional importance of the secular state, which means respecting the freedom of religious choice. Also, we advocate the separation of church and state.
c) We understand that the Agreement between the Federative Republic of Brazil and the Holy See violates the principles of Article 19 of the Brazilian Constitution of 1988. [quoted above]
d) We urge the Brazilian Senate not to approve the Agreement between the Holy See and the Brazilian Republic in order to guarantee the Constitutional precepts. [...]
Human Rights Commission of the Brazilian Magistrates rejects the concordat
Associação dos Magistrados Brasileiros, 14 August 2009
The National Commission for Human Rights of the Association of Brazilian Magistrates (AMB), composed of representatives of all affiliated entities, publicly expresses support for opposition to the incorporation into the Brazilian legal system of the Agreement between Brazil and the Vatican.
The AMB points out that the current constitutional model has established the secularism of the Brazilian state, guaranteeing religious freedom to all citizens. Its acceptance by the National Congress [...] will cause a serious setback to the exercise of freedoms and the [legal] validity of diversity as a fundamental principle of the state. We ask that the Legislature treat this matter in a strictly constitutional manner.
Mozart Valadares Pires
President of the AMB
1. These included: Ação Educativa, Associação Brasileira de Antropologia, Associação Brasileira de Ateus e Agnósticos, Associação Brasileira de Defesa da Laicidade do Estado, Associação Brasileira de Gays, Lésbicas, Bissexuais, Travestis e Transexuais, Associação Brasileira de Liberdade Religiosa e Cidadania, Associação Brasileira de Templos de Umbanda, Associação dos Magistrados Brasileiros, Associação dos Pastores Evangélicos do Piauí, Católicas pelo Direito de Decidir, Conselho Regional de Assistentes Sociais/SP, Fórum Estadual de Defesa dos Direitos da Criança e do Adolescente -SP, Sindicato dos Professores do Ensino Oficial do Estado de São Paulo, Superior Órgão de Umbanda de São Paulo.
“Sociedade civil se mobiliza contra concordata Brasil-Vaticano”, Fórum de Entidades Nacionais de Direitos Humanos, 2009-10-22. http://www.direitos.org.br/index.php?option=com_content&task=view&id=5435&Itemid=2
2. “No terreiro canta banho de manjericão”, the title, means “singing in the shrine about baths of basil”. It refers to the practice of bathing in infusions of basil to try to get rid of “negativity” and increase “personal power”. The song was recorded in 1979 at the Casa de Candomblé Ilê Alafin Ixé. http://www.youtube.com/watch?v=ThhIeGnIaV0&feature=autoplay&list=PL108711B6FEAEDE3F&playnext=1 Instructions for “banho de manjericão”, are given on many sites, for instance: http://ciganadaminhaura.blogspot.no/2010/02/banho-de-limpeza-manjericao.html
3. “Terreiros lutam por direitos históricos”, Camara Municipal de Salvador, 2013-09-27. http://www.cms.ba.gov.br/noticia_int.aspx?id=6704
4. Some articles of the Brazilian concordat are clearer in one translation, others in another one. The two used here are: