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:
CASE SNAPSHOT
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.
STATUS
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:
