From Resolution 2253 (Jan. 22, 2019), "Sharia, the Cairo Declaration and the European Convention on Human Rights":
[4.] The Assembly considers that the various Islamic declarations on human rights adopted since the 1980s, while being more religious than legal, fail to reconcile Islam with universal human rights, especially insofar as they maintain the Sharia law as their unique source of reference. This includes the 1990 Cairo Declaration on Human Rights in Islam, which, whilst not legally binding, has symbolic value and political significance in terms of human rights policy under Islam. It is therefore of great concern that three Council of Europe member States—Albania, Azerbaijan and Turkey (with the limitation "so far as it is compatible with its laws and its commitments under international conventions")—have endorsed, explicitly or implicitly, the 1990 Cairo Declaration, as have Jordan, Kyrgyzstan, Morocco and Palestine, whose parliaments enjoy partner for democracy status with the Assembly.
[5.] The Assembly is also greatly concerned about the fact that Sharia law—including provisions which are in clear contradiction with the Convention—is applied, either officially or unofficially, in several Council of Europe member States, or parts thereof.
[6.] The Assembly recalls that the European Court of Human Rights has already stated in Refah Partisi (The Welfare Party) and others v. Turkey that "the institution of Sharia law and a theocratic regime were incompatible with the requirements of a democratic society". The Assembly fully agrees that Sharia law rules on, for example, divorce and inheritance proceedings are clearly incompatible with the Convention, in particular its Article 14, which prohibits discrimination on grounds such as sex or religion, and Article 5 of Protocol No. 7 to the Convention (ETS No. 117), which establishes equality between marital partners. Sharia law is also in contradiction with other provisions of the Convention and its additional protocols, including Article 2 (right to life), Article 3 (prohibition of torture or inhuman or degrading treatment), Article 6 (right to a fair trial), Article 8 (right to respect for private and family life), Article 9 (freedom of religion), Article 10 (freedom of expression), Article 12 (right to marry), Article 1 of Protocol No. 1 (ETS No. 9) (protection of property) and Protocols Nos. 6 (ETS No. 114) and 13 (ETS No. 187) prohibiting the death penalty.
[7.] In this context, the Assembly regrets that despite the recommendation it made in its Resolution 1704 (2010) on freedom of religion and other human rights for non-Muslim minorities in Turkey and for the Muslim minority in Thrace (eastern Greece), asking the Greek authorities to abolish the application of Sharia law in Thrace, this is still not the case. Muftis continue to act in a judicial capacity without proper procedural safeguards. The Assembly denounces in particular the fact that in divorce and inheritance proceedings—two key areas over which muftis have jurisdiction—women are at a distinct disadvantage.
[8.] The Assembly is also concerned about the "judicial" activities of "Sharia councils" in the United Kingdom. Although they are not considered part of the British legal system, Sharia councils attempt to provide a form of alternative dispute resolution, whereby members of the Muslim community, sometimes voluntarily, often under considerable social pressure, accept their religious jurisdiction mainly in marital and Islamic divorce issues, but also in matters relating to inheritance and Islamic commercial contracts. The Assembly is concerned that the rulings of the Sharia councils clearly discriminate against women in divorce and inheritance cases. The Assembly is aware that informal Islamic Courts may exist in other Council of Europe member States too.
[9.] The Assembly calls on the member States of the Council of Europe to protect human rights regardless of religious or cultural practices or traditions on the principle that where human rights are concerned, there is no room for religious or cultural exceptions....
[11.] The Assembly calls on Council of Europe member States and those whose parliaments enjoy partner for democracy status with the Assembly to:
[11.1] bolster pluralism, tolerance and a spirit of openness by proactive measures, taken by governments, civil society and religious communities, whilst respecting common values as reflected in the European Convention on Human Rights;
[11.2] design and implement educational and vocational programmes aimed at rooting human rights and fundamental freedom as enshrined in the Convention, and in particular the principles of gender equality and of non-discrimination based on religious beliefs, in the cultural and legal tradition of their countries;
[11.3] promote, within the multilateral organisations of which they are members or observers, the universal values of human rights without any discrimination based inter alia on sex, gender, sexual orientation, gender identity, and religious faith or the lack of it;
[11.4] engage in the process of revision of the Cairo Declaration launched by the Organisation of Islamic Cooperation (OIC) so as to ensure that the future OIC Declaration on Human Rights is compatible with universal human rights standards and the European Convention on Human Rights which is binding on all Council of Europe member States and a source of inspiration for those whose parliaments enjoy partner for democracy status.
 The Assembly calls on Albania, Azerbaijan and Turkey, to consider distancing themselves from the 1990 Cairo Declaration by:
[12.1] considering withdrawing from the Cairo declaration;
[12.2] making use of all available means to make declarations, so as to ensure that the 1990 Cairo Declaration has no effect on their domestic legal orders that may be inconsistent with their obligations as Parties to the European Convention on Human Rights; or
[12.3] considering performing some formal act which clearly establishes the Convention as a superior source of obligatory binding norms.
 The Assembly, while noting the legislative change in Greece which made the practice of Islamic sharia law in civil and inheritance matters optional for the Muslim minority, calls on the Greek authorities to:
[13.1] rapidly and fully implement the Grand Chamber judgment of the European Court of Human Rights in the case of Molla Sali v. Greece and in particular, to monitor whether the above-mentioned legislative change will be sufficient to satisfy the requirements of the Convention;
[13.2] allow the Muslim minority to choose freely its muftis as purely religious leaders (that is, without judicial powers), through election, thereby abolishing the application of Sharia law, as already recommended in Resolution 1704 (2010).
 The Assembly, while welcoming the recommendations put forward in the conclusions of the Home Office Independent review into the application of sharia law in England and Wales, as a major step towards a solution, calls on the authorities of the United Kingdom to:
[14.1] ensure that Sharia councils operate within the law, especially as it relates to the prohibition of discrimination against women, and respect all procedural rights;
[14.2] review the Marriage Act to make it a legal requirement for Muslim couples to civilly register their marriage before or at the same time as their Islamic ceremony, as is already stipulated by law for Christian and Jewish marriages;
[14.3] take appropriate enforcement measures to oblige the celebrant of any marriage, including Islamic marriages, to ensure that the marriage is also civilly registered before or at the same time as celebrating the religious marriage;
[14.4] remove the barriers to Muslim women's access to justice and step up measures to provide protection and assistance to those who are in a situation of vulnerability;
[14.5] put in place awareness campaigns to promote knowledge of their rights amongst Muslim women, especially in the areas of marriage, divorce, custody of children and inheritance, and work with Muslim communities, women organisations and other non-governmental organisations to promote gender equality and women's empowerment;
[14.6] conduct further research on "judicial" practice of Sharia councils and on the extent to which such councils are used voluntarily, particularly by women, many of whom would be subject to intense community pressure in this respect....
Thanks to Prof. Howard Friedman (Religion Clause) for the pointer.