Yes, Methodists do have doctrinal standards

AN EXPLANATION OF THE FOUNDATIONS OF THE DOCTRINAL STANDARDS OF THE UNITED METHODIST CHURCH
(specifically, as it pertains to my understanding of the Church's relationship to the issues of open sexuality)

by Bruce Ferguson

The United Methodist Church, as an organization, is defined by the contents of The Book Of Discipline. At the heart of this definition are 6 paragraphs in the Discipline known as the Restrictive Rules. The legislative requirements to change them are are so tough that it would take an Act of God to do so. It is safe to say that, whatever else gets debated in the Church, arguing about the need to change these will truly be a waste of time. The first one of these is

¶ 17. Article I.—The General Conference shall not revoke, alter, or change our Articles of Religion or establish any new standards or rules of doctrine contrary to our present existing and established standards of doctrine.

Since the first American Methodist Conference in 1773 Wesley's Explanatory Notes and Standard Sermons have been accepted as doctrinal standards. These, along with the Articles of Religion, were codified as standards at the Constitutional Conference of 1808. Although the precise number of sermons was never clearly stated, it has been accepted that the collection published in 1843 by Thomas Jackson as Series 1, which includes 53 sermons, is appropriately authoritative.
The 25 Articles Of Religion are the result of Wesley editing down the 39 Articles of the Church of England to that which would be appropriate for a church free from the rule of the King of England.
THE STANDARDS OF DOCTRINE THAT SEEM TO APPLY TO THIS ISSUE.
(Specifically, language that would be more inclusive of the GLBTQ community)

Article 6—Of the Old Testament (From the Articles of Religion)
“The Old Testament is not contrary to the New; for both in the Old and New Testament everlasting life is offered to mankind by Christ, who is the only Mediator between God and man, being both God and Man. Wherefore they are not to be heard who feign that the old fathers did look only for transitory promises. Although the law given from God by Moses as touching ceremonies and rites doth not bind Christians, nor ought the civil precepts thereof of necessity be received in any commonwealth; yet notwithstanding, no Christian whatsoever is free from the obedience of the commandments which are called moral.”

The Mosaic Law (that which is understood to have been given to Moses from God on Mount Sinai) which begins in Exodus 20 and continues on through Leviticus, Numbers, and Deuteronomy has been divided into three parts (by both Jewish and Christian theologians) with remarkable consistency. The Law is divided into the civil, the ceremonial, and the moral parts. The proscriptions against same-gender relations in Leviticus 18 and 20 are understood to be part of the moral law.
The following Standard Sermons are instructive as to the proper understanding of the moral law in the Christian's life. Simply put, Wesley contends that the moral law was in place long before the giving of The Law to Moses; that this giving of The Law merely codified the moral code God expected all humans to live by from the very beginning, and that the new covenant of Jeremiah 31:31-34 that was to write God's law on our hearts was in fact the Holy Spirit bringing this code in all its fullness to every Christian's personal awareness. Therefore, any teaching that we were no longer expected to be moral according to this is an abomination to God.

Standard Sermon 25, 5^th Discourse on the Sermon of the Mount (Matthew 5:17-20)

Standard Sermon 34, The Original, Nature, Property, and Use of the Law

And from Wesley's Explanatory Notes:

(from Wesley's Notes on the New Testament; 1 Peter 4:11) “The oracles of God teach that men should repent, believe, obey. He that treats of faith and leaves out repentance, or does not enjoin practical holiness to believers, does not speak as the oracles of God: he does not preach Christ, let him think as highly of himself as he will.”
(from Wesley's Notes on the New Testament; 1 Timothy 1:8) “We grant the whole Mosaic law is good, answers excellent purposes, if a man use it in a proper manner. Even the ceremonial is good, as it points to Christ; and the moral law is holy, just, and good, on its own nature; and of admirable use both to convince unbelievers, and to guide believers in all holiness.”
Bishop Scott Jones wrote the book on United Methodist doctrine. In United Methodist Doctrine: The Extreme Center he writes:

“If dissent from doctrine involves disagreement with something very close to the center of the Church’s teaching and attempts to get the Church to change its teaching fail, then a responsible person will surrender his or her conference relationship and leave the Church. Rather than preach a unitarian understanding of God, theories of white supremacy, or other doctrines contrary to the core teachings of the Church, persons of integrity will come to the conclusion that they do not belong as a representative of the United Methodist Church and should in good conscience join another religion. There are certain beliefs like the Trinity and God’s love for persons of all races that are so central to the United Methodist understanding of the gospel that fundamental disagreement with them requires the breaking of fellowship. This is the spiritual basis for the chargeable offense in ¶2702, 'dissemination of doctrines contrary to the established standards of doctrine of The United Methodist Church.' In cases where doctrinal dissent is so fundamental and yet the dissenter will not voluntarily leave the Church, the Church must protect the integrity of its own witness by removing the person from its fellowship.” (United Methodist Doctrine-The Extreme Center, Scott J. Jones; p294; Chapter 10: “Preaching and Maintaining United Methodist Doctrine”)

As a member of The United Methodist Church, I believe that I am constrained by our Discipline by specific doctrinal standards. These are not up for a vote, nor are they meant to be disregarded. This is who we are. I know that not all communities of Christian faith are so constrained. However, as an act of integrity, when i call myself United Methodist, I acknowledge the authority of these standards. Therefore, as a minister within The United Methodist Church, I am morally obligated to limit my preaching, teaching, and behavior to that which does not go counter to these standards.

To be completely open, our Book of Discipline offers the following instructions to the Church to govern its daily life:

¶ 4. Article IV. Inclusiveness of the Church
The United Methodist Church is a part of the church universal, which is one Body in Christ. The United Methodist Church acknowledges that all persons are of sacred worth. All persons without regard to race, color, national origin, status, or economic condition, shall be eligible to attend its worship services, participate in its programs, receive the sacraments, upon baptism be admitted as baptized members, and upon taking vows declaring the Christian faith, become professing members in any local church in the connection. In The United Methodist Church no conference or other organizational unit of the Church shall be structured so as to exclude any member or any constituent body of the Church because of race, color, national origin, status or economic condition.

¶ 214. Eligibility
The United Methodist Church is a part of the holy catholic (universal) church, as we confess in the Apostles' Creed. In the church, Jesus Christ is proclaimed and professed as Lord and Savior. All people may attend its worship services, participate in its programs, receive the sacraments and become members in any local church in the connection (¶ 4). In the case of persons whose disabilities prevent them from reciting the vows, their legal guardian[s], themselves members in full covenant relationship with God and the Church, the community of faith, may recite the appropriate vows on their behalf.

¶ 304.3 Qualifications for Ordination
While persons set apart by the Church for ordained ministry are subject to all the frailties of the human condition and the pressures of society, they are required to maintain the highest standards of holy living in the world. The practice of homosexuality is incompatible with Christian teaching. Therefore self-avowed practicing homosexuals¹ are not to be certified as candidates, ordained as ministers, or appointed to serve in The United Methodist Church.1. "Self-avowed practicing homosexual" is understood to mean that a person openly acknowledges to a bishop, district superintendent, district committee of ordained ministry, board of ordained ministry, or clergy session that the person is a practicing homosexual.

¶ 806.9 Fiscal Responsibilities [of the General Council on Finance and Administration]
[The General Council on Finance and Administration] shall be responsible for ensuring that no board, agency, committee, commission, or council shall give United Methodist funds to any gay caucus or group, or otherwise use such funds to promote the acceptance of homosexuality or violate the expressed commitment of The United Methodist Church "not to reject or condemn lesbian and gay members and friends" (¶ 161F). The council shall have the right to stop such expenditures. It shall not limit the Church's ministry in response to the HIV epidemic.

These paragraphs are not part of the Restrictive Rules, and as such, continue to be refined by General Conference every four years. However, to the extent that they fall within the area of doctrine, such refinement can be expected to fall within the parameters of our Doctrinal Standards.

The Church Of 1955 (CO55)

Doesn't ANYBODY in the church know it's the 21st Century?

The acclaim for the new Wesley Study Bible is impressive. Having just read the list of contributors, I must admit that I don't know most of them, but the names I recognize I respect. And although reviews of this Bible are mixed, I suspect that this Bible would have made leading Bible studies 20 or 30 years ago more productive in advancing the Wesleyan message. Remember those Bible studies? There would always be one spiritual giant who would not only know his or her Bible, but would quote authoritatively from the study notes written by Mr. Scofield or Mr. Ryrie. Which would be fine if we were all 5-Point Calvinistic Dispensationalists, but we weren't. Some of us were just reading and studying the Bible. We didn't start with Calvin's presuppositions, so we didn't see the absolute predestination. We didn't start with Mr. Darby's presuppositions, so we don't have this dogmatic need to try to explain why God has done certain things at certain times, and why we can expect Him to do things (or refrain from doing things) in the future.