The First Amendment to the US constitution says:

Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the government for a redress of grievances.

The clause pertaining to religion states that “Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof” which means that there are two parts, what have come to be known as the Establishment Clause and the Free Exercise Clause. It is the Establishment Clause that has come under stress recently as religious zealots in the US, convinced that this is a Christian country, seek to make that manifest by having prayers at government functions, putting up Ten Commandments monuments in public spaces, putting mottoes like ‘In God We Trust’ on currency and elsewhere, and placing nativity scenes at Christmas time.

The US Supreme Court’s responses to the cases have been muddled, to put it frankly. They seem to struggle to find ways to accommodate at least some religious invasion of the public sphere, even if it leads to convoluted reasoning, possibly out of a sense that outright prohibition might cause too much of a furor.

Scotusblog had a symposium on how the current composition of the US Supreme Curt might view the religion clauses and I found this contribution by Erwin Chemerinsky, Dean of University of California, Berkeley School of Law, to be informative.

He first discusses the Establishment Clause.

For at least the last few decades, the justices have been split among three different theories as to when government actions violate the establishment clause. The conservative justices have argued that the establishment clause is violated only if the government coerces religious participation or the government discriminates among religions in giving financial benefits. Under this approach, for example, religious symbols on government property do not infringe the First Amendment because they do not coerce religious participation. Also, under this approach, the government cannot deny religious institutions benefits that are provided to secular private institutions.

The liberal justices, by contrast, have contended that the establishment clause, in the words of Thomas Jefferson, creates a wall between church and state. These justices believe that religious symbols do not belong on government property. They do not believe that the government should be able to give aid to religious institutions if it is a type that might be used for religious instruction.

In the middle between these two views was the position that establishment clause means that the government cannot endorse religion or a particular religion. Justice Sandra Day O’Connor initially articulated this approach and followed it throughout her time on the Supreme Court. Under this approach, the question is whether a particular symbol would be regarded by the reasonable observer as an endorsement of religion. Also, this approach would allow the government to provide aid to religious schools so long as it is not actually used for religious instruction.

He thinks that Neil Gorsuch and Brett Kavanaugh would rule on Establishment Clause cases the same way as the people they replaced (Antonin Scalia and Anthony Kennedy), thus maintaining the current somewhat confused state.

But when it comes to the Free Exercise Clause, he thinks there may be changes.

In 1990’s Employment Division v. Smith, the Supreme Court, in a majority opinion by Scalia, held that the free exercise clause cannot be used to challenge a neutral law of general applicability. In other words, so long as a law is neutral in that it is not motivated by a desire to interfere with religion and so long as it applies to everyone, the free exercise clause cannot be used to challenge it no matter how much it burdens religion. In Employment Division v. Smith, the court ruled against Native Americans who were challenging an Oregon law that prohibited the use of peyote, something that they said was required in their religious rituals. The court ruled against the Native Americans by concluding that the Oregon law was neutral and of general applicability.

But now, there well may be a majority on the Supreme Court willing to overrule Employment Division v. Smith and provide more constitutional protection for free exercise claims.

He concludes:

Views on issues concerning the Constitution and religion very much divide along ideological lines. I predict that Gorsuch and Kavanaugh will adopt the position of a very weak establishment clause and a free exercise clause that provides robust protection of religion. The former view will resemble that advanced by Scalia and Kennedy, but the latter may bring about a significant change in the law.

So we will likely see a tilt towards more accommodation of religion, at least as far as the Free Exercise of religion goes.