Who adheres to dual-covenant theology?

Scholars or groups who directly adhere to the Dual Covenant Theology

Those churches or scholars who agree with the statements of the Council of Centers on Jewish-Christian Relations (CCJR)

The Christian Scholars Group on Christian-Jewish Relations is an ecumenical gathering of about twenty Christian academicians who since 1969 have been exploring the theological relationship between Judaism and Christianity. In 2002 it released this statement, which was partially intended as a complement to a Jewish statement on Christians and Christianity, Dabru Emet, issued two years earlier. The CSG subsequently published a collection of essays that expands upon the principles listed below, entitled Seeing Judaism Anew: Christianity's Sacred Obligation.

Some points from the statement:

5. The Bible both connects and separates Jews and Christians.

Some Jews and Christians today, in the process of studying the Bible together, are discovering new ways of reading that provide a deeper appreciation of both traditions. While the two communities draw from the same biblical texts of ancient Israel, they have developed different traditions of interpretation. Christians view these texts through the lens of the New Testament, while Jews understand these scriptures through the traditions of rabbinic commentary.

Referring to the first part of the Christian Bible as the "Old Testament" can wrongly suggest that these texts are obsolete. Alternative expressions - "Hebrew Bible," "First Testament," or "Shared Testament" -- although also problematic, may better express the church's renewed appreciation of the ongoing power of these scriptures for both Jews and Christians.

6. Affirming God's enduring covenant with the Jewish people has consequences for Christian understandings of salvation.

Christians meet God's saving power in the person of Jesus Christ and believe that this power is available to all people in him. Christians have therefore taught for centuries that salvation is available only through Jesus Christ. With their recent realization that God's covenant with the Jewish people is eternal, Christians can now recognize in the Jewish tradition the redemptive power of God at work. If Jews, who do not share our faith in Christ, are in a saving covenant with God, then Christians need new ways of understanding the universal significance of Christ.

7. Christians should not target Jews for conversion.

In view of our conviction that Jews are in an eternal covenant with God, we renounce missionary efforts directed at converting Jews. At the same time, we welcome opportunities for Jews and Christians to bear witness to their respective experiences of God's saving ways. Neither can properly claim to possess knowledge of God entirely or exclusively.

It is surprising that a recent controversial Roman Catholic document released in 10 December 2015 also seems to assume DCT as it discourages evangelism to Jews. However the Vatican also clarified that it is not a "doctrinal teaching of the Catholic Church," but a reflection based on doctrine and flowing from Vatican II's declaration "Nostra Aetate" on Catholic relations with other religions. It seems these views are rather in the line of liberal and secular trend under Pope Francis which many times seems to be inclusive towards all religions and lifestyles. It has been strongly criticized by some Christians scholars.

The motivation behind DCT may be the combination of both (1) trying to find Jewish roots of Christianity and (2) reconcile the fate of good people who die outside of faith in Christ.

Quote from wikipedia - Dual-covenant_theology

David H. Stern, a Messianic Jewish theologian, wrote that dual-covenant theology is said to originate with Maimonides. It was proffered in the 20th century by the Jewish philosopher Franz Rosenzweig, and was elaborated upon by such theologians as Reinhold Niebuhr and James Parkes.

These founders believe that Jesus' message is not for Jews but for Gentiles and, that John 14:6 is to be understood thusly: "I am the way, the truth and the life; and no Gentile comes to the father except through me."[9] Stern asserts that the problem of dual-covenant theology is that "replacing Yeshua’s 'No one comes to the Father except through me' with 'No Gentile comes...' does unacceptable violence to the plain sense of the text and to the whole New Testament."[10]

In the comment right above yours in the referenced question, What is the biblical basis for dual-covenant theology? (I'm sorry I can't link because I don't have enough rep and I need to save them for references below), the author answers the first part of your question and his references in that question apply as well.

"Also bear in mind that proponents of DCT rarely refer to it as "dual covenant theology" themselves, it is mostly used as a pejorative by opponents of this school of thought. Another term often used is the German word Sonderweg, so I suggest you also use that as a search term. DCT is the standard position of denominations of traditional Judaism (eg, Conservative, Modern Orthodox, Haredi, Hasidic, etc), and is popular among some segments of Liberal Protestantism and Messianic Jewish movements. – Meir Illumination Aug 15 '15 at 5:34"

I have also noticed some "liberal" Baptist preachers that I mention below.

For the second part as to who specifically in Christian faiths espoused DCT, it seems to be a dirty term because none of the pastors will admit to believing in DCT when asked directly, but the teaching speaks a different story.

Pastor Jerry Falwell, Pat Robertson, and John Hagee are just three prominent names. Many many more are listedoing in an article here. http://www.jpost.com/Jewish-World/Jewish-News/Falwell-Jews-can-get-to-heaven and here https://healtheland.wordpress.com/2008/02/14/pat-robertson-dual-covenant-theology-heretic/ (again I apologize I can only provide two links because of my low rep so I can't expound much farther without being in danger of making statements without enough reference quotes)