The highest profile case, of course, was Little Sisters of the Poor v. Commonwealth of Pennsylvania. The Little Sisters of the Poor have been a target of intense persecution by the Left and the legal "resistance". This excerpt from the Becket Fund web site gives you the picture:
Despite a 2016 victory at the U.S. Supreme Court, an Executive Order, and a new rule that protects the Little Sisters of the Poor and other non-profit religious groups from the unconstitutional HHS mandate, the Little Sisters are still in court. In November 2017, after the federal government issued their new rule protecting religious groups from the mandate, the Commonwealth of Pennsylvania and several other states sued in federal court to take away the nuns’ hard-won religious exemption. Becket intervened on behalf of the Little Sisters, arguing that the states have no right to challenge the new rule. Oral argument was held on March 23, 2018 to decide whether the Sisters will be allowed to intervene in the case, and on April 24, 2018, the Little Sisters’ motion for intervention was granted.
On July 12, 2019, the Third Circuit ruled against the Little Sisters. On October 1, 2019, the Little Sisters of the Poor asked the Supreme Court to protect them from the HHS contraceptive mandate again and end their legal battle once and for all. The Supreme Court heard oral argument in Little Sisters of the Poor v. Commonwealth of Pennsylvania on May 6, 2020. On June 8, 2020 the Court ruled 7-2 in favor of the Little Sisters of the Poor.
I will note that the Little Sisters case (the other case being Our Lady Of Guadalupe School v. Morrissey-Berru) was decided on the basis of the RFRA (Right to Religious Freedom Act) and the ACA (Obamacare), rather than First Amendment issues. Footnote #10 in the Little Sisters case states:
The dissent claims that “all agree” that the exemption is not supported by the Free Exercise Clause. ... A constitutional claim is not presented in these cases, and we express no view on the merits of that question.
Clarence Thomas wrote the majority opinion in the Little Sisters case, Alito in the Our Lady of Guadalupe case. Thomas wrote:
"For over 150 years, the Little Sisters have engaged in faithful service and sacrifice, motivated by a religious calling to surrender all for the sake of their brother," Thomas wrote. "But for the past seven years, they—like many other religious objectors who have participated in the litigation and rulemakings leading up to today’s decision— have had to fight for the ability to continue in their noble work without violating their sincerely held religious beliefs."
However, the decision in Our Lady of Guadalupe was based on the First Amendment's Free Exercise clause, and is potentially extremely important. Jonathan Turley notes the broad scope of the decision:
Big win (7-2) for religious organizations with an opinion by Justice Alito in Our Lady of Guadalupe School v. Morrissey Berru. "The First Amendment's Religion Clauses foreclose the adjudication of [the teachers'] employment-discrimination claims."
What is notable is that the Court rules for the school despite the fact that "these teachers were not given the title of 'minister' and have less religious training than" than the teacher in its earlier Hosanna-Tabor decision. That gives even more leeway and protection for schools.
Held: The First Amendment’s Religion Clauses foreclose the adjudication of Morrissey-Berru’s and Biel’s employment-discrimination claims. Pp. 10–27.
(a) The independence of religious institutions in matters of “faith and doctrine” is closely linked to independence in what the Court has termed “‘matters of church government.’” Hosanna-Tabor, 565 U. S., at 186. For this reason, courts are bound to stay out of employment disputes involving those holding certain important positions with churches and other religious institutions.
This 7-2 decision gives powerful protection to counter-cultural institutions--whether Catholic, Jewish, or Protestant--that have been under continual assault in recent years.
And, again, make no mistake about it--these decisions are major victories for Trump, especially in this election year.