Burke has opined that Catholic politicians who support legalized abortion, including American presidential candidate John Kerry and United States President Joe Biden, should not receive the Eucharist.

In 1989, Pope John Paul II named Burke as the first American defender of the bond of the Supreme Tribunal of the Apostolic Signatura, the highest ecclesiastical court in the Catholic Church.

In reaction, Burke stated that: "our tiniest brothers and sisters ... will be made legally the subjects, the slaves, of those who wish to manipulate and destroy their lives for the sake of supposed scientific and technological progress.

[13] In February 2017, Burke presided over a five-judge panel at the church trial of Archbishop Anthony Sablan Apuron of the Diocese of Agaña in Guam on charges of sexual abuse of minors.

[11][12] According to a 2015 article in National Catholic Reporter (NCR), some bishops have refused permission for Burke to host conferences in their dioceses, and that a number of priests have accused him of "spreading propaganda against the Pope".

In a July 2019 editorial, the NCR rebuked Burke for wanting to "reconstitute the clericalism that is at the heart of the sex abuse cover-up scandal that continues to undermine the authority of the church."

"[12] NCR labeled him as:"the modern version of that religious leader that drew some of Jesus' harshest condemnations, those who placed undue burdens on others and pronounced themselves the undisputed bearers of truth.

[74] On June 10, 2019, Burke, Cardinal Jānis Pujats, and Bishops Tomasz Peta, Jan Paul Lenga, and Athanasius Schneider published a 40-point "Declaration of Truths" that claimed to reaffirm traditional church teaching.

"[81] In an October 17, 2014, interview with BuzzFeed News, Burke said that if "Pope Francis had selected certain cardinals to steer the meeting [synod] so as to advance his personal views on matters like divorce and the treatment of LGBT people", he would not be observing his mandate as the leader of the Catholic Church.

On June 10, 2019, Burke, Cardinal Jānis Pujats, and bishops Tomasz Peta, Jan Paul Lenga, and Athanasius Schneider published a 40-point "Declaration of Truths" claiming to reaffirm traditional church teaching.

Burke and Schneider criticized the document for its "implicit pantheism," support for married clergy and a greater role for women in the liturgy, and for what they considered to be excessive openness to pagan rituals and practices common among the Amazonian peoples.

[83] In 2007, the singer Sheryl Crow, an advocate for embryonic stem-cell research, was scheduled to perform at a benefit concert for the Cardinal Glennon Children's Hospital in St. Louis.

[86] Burke in June 2004 clarified his position, stating that one could vote for a pro-abortion politician and not commit a mortal sin, if one believed there was a more significant moral issue than abortion at hand.

[87] In a September 2008 interview with Catholic News Service, Burke said that "the Democratic Party risks transforming itself definitively into a 'party of death', because of its choices on bio-ethical questions", especially elective abortion.

Burke said Marx's remarks showed how the church lacked "the clarity and the courage to announce the Gospel of Life and Divine Love to the radically secularized culture".

Burke alluded to so-called diabolical errors spreading from society to Church leaders, raising concerns that the "end times" were nearing, and once again stating that homosexual acts were sinful.

"[74] In February 2019 Burke penned an open letter with Cardinal Walter Brandmuller addressed to Francis, calling for an end of "the plague of the homosexual agenda," which they blamed for the sexual abuse crisis engulfing the Catholic Church.

Think of the early Councils, the Arian heresy, for instance, when Athanasius even became physically aggressive”, Burke also mentioned that John Paul II had ruled out women's ordination “once and for all”.

[109] Burke, along with three other cardinals, issued a set of dubia, or doubts, to Francis, asking him to clarify various points of doctrine in his 2016 apostolic exhortation, Amoris laetitia and on general Christian life.

Since the 2014 synod, some bishops had begun allowing Catholics who had been divorced and remarried to receive the eucharist, despite the fact that such persons are traditionally said to be committing adultery and living in mortal sin and therefore ineligible to participate according to official church law.

"[113] The four cardinals submitted the dubia in private, followed by a public letter ("Seeking Clarity: A Plea to Untie the Knots in Amoris Laetitia") in November 2016, asking Francis to clarify various points of doctrine.

[117] On April 7, 2018, Burke, along with Brandmüller and Schneider, participated in a conference rejecting the outline proposed by German bishops to allow divorced and remarried Catholics to receive the eucharist.

Citing chapter 19 of the Gospel of Matthew, Burke disputed the notion that anyone, including the pope, had the authority to accept divorced and remarried Catholics as full members of the church.

"[126][127] At the same time, Burke is known to wear lavish regalia and "is one of the few cardinals who dons cappa magnas, the long trains of watered silk that can look like scarlet lava flowing down from his throne" as well as "velvet gloves and extravagant brocades.

[104]Burke condemned Traditionis custodes, a July 2021 motu proprio issued by Francis which effectively reversed Summorum Pontificum by placing limits on priests offering the Traditional Form of the Mass.

He alleged that Francis' document was "marked by harshness" towards those who attend mass in the older form and criticized the fact that it took effect immediately, which in his view did not give adequate time for those affected to study its meaning.

In written comments to the synod, Burke criticized "antinomianism", the belief that grace exempts Christians from obedience to moral law, stating that it is "among the most serious wounds of society today," and is responsible for the legalization of "intrinsically evil" actions such as abortion, embryonic stem-cell research, euthanasia, and same-sex marriage.

[137] In 2019, however, Burke resigned from the board and cut ties with Bannon because of the latter's stated intent to make a film adaptation of Frederic Martel's work In the Closet of the Vatican.

In 2017, Burke met with the right-wing Italian nationalist Matteo Salvini, head of Italy's Northern League and an opponent of Francis on immigration and dialogue with Muslims.

[74] In 2019, Burke was reported to have received, together with other influential U.S. Catholic leaders, substantial monetary gifts from West Virginia bishop Michael J. Bransfield, who had resigned following allegations of sexual misconduct.