Yes, but it was probably considered uncommon by the time of the American Revolution.
Crimes against nature
Even after the American Revolution, statutes remained on the books of numerous U.S. states that imposed the death penalty not just for murder, but for some crimes of sexual sin, paralleling those in Leviticus 20, sometimes quoting directly from religious text. Details of enforcement are scanty, because they were considered "the crime not fit to be named among Christian men." However, lack of evidence is not evidence of absence. In some sense all capitol punishment might be considered killing justified by religion in any religion based on the Old Testament, we've just found alternate words to describe it. Others of course argue it is not justified, I take no position one way or the other.
The Witchcraft Act 1735, was intended to end executions for most religious crimes under the laws of the Kingdom of Great Britain, but the practice continued to be permitted in other monarchies, typically for heresy, which we would view today as a religious crime. The primary example might be heresy against the Roman Catholic church under Spanish law.
The Spanish Inquisition had extended into New Spain (including North America) and was known as the Mexican Inquisition. That religious court was established in Mexico City and only abolished in 1820, as a result of Mexican independence.
By 1781 under Spanish law, heresy against the Roman Catholic church was still legally punishable by execution by burning, but that was generally considered unseemly, so heretics were sometimes granted the privilege of being strangled before the flames were lit.
Records of the Inquisition in Mexico are at best incomplete, however researchers have said that while the Mexican Inquisition only prosecuted a very small portion of the population, the persecution of crypto-Judaism was one of the more dramatic kinds of spectacles because they usually ended in death, especially during the early period.
In Europe, Cayetano Ripoll is thought to be the last heretic executed by the Spanish Inquisition, he was garrotted in 1826 Spain for teaching Deist principles in violation of the teachings of the church. So while it seems unclear if killings based entirely on religious beliefs were happening in the New World in the time of the founding fathers, they certainly had good reason to believe the threats remained.
Several of the US founding fathers were heavily involved with Deist principles including James Madison and Thomas Paine. The later is especially relevant as after the American Revolution, Paine moved to France, and during the revolution there was imprisoned and targeted for execution based on his own Deist writings collected as The Age of Reason. Paine was released only through the diplomatic intervention of James Monroe (another founding father and future president) in 1794.
Other founding fathers including Benjamin Franklin, George Washington and Thomas Jefferson were at least interested in Deist principals deemed heritical by the Catholic church. So yes, it can be said that questioning the teachings of organized religion of the day could result in a death sentance, and that fact led to inclusion of religious tolerance and freedom in the US constitution.
Anticatholicism in America
The story is not as one-sided as it might seem. It should be noted however that colonies like Maryland, founded by the Catholic Lord Baltimore passed the Maryland Toleration Act of 1649. However this was done in an effort to protect English Catholic settlers as the Catholic population quickly became a minority. The Puritans took power and permanently revoked the tolerance act until the American revolutions. During that time, the Catholics of Maryland were subject to persecution based on their religion with corporal punishment, though probably not death for heresy due to the 1735 act in Britain. But prior to that, a number of people had been executed in Puritan states, including a group of women known as the Boston martyrs who were condemned to death and executed by public hanging for repeatedly entering the Massachusetts Bay Colony as Catholics about a century earlier.
Treason and the Devine Rights of Kings
The European concept of the Devine Right of Kings held that a King received his authority to rule from God. In 1534, Parliament passed the Act of Supremacy and the Treasons Act, establishing correspondingly the King's religious position in the law, and making it an act of treason, punishable by death to disavow that supremacy. Though exercised in the 1500s, this law became dormant and religious tolerance in England took hold, but remained on the books.
In 1760 Francis Bernard became Governor of Massachusetts, and in 1765, he wrote that the King-in-Parliament retained power that was absolute, uncontrollable, and accountable to none, and therefore, in a political sense, can do no wrong. He also asserted that this applied unconditionally in the American Colonies of the Kingdom, regardless of their lack of representation in Parliament.
One of the final issues leading to the American Revolution was the Administration of Justice Act 1774, which George Washington and others referred to as the Murder Act, as they thought it permitted the murder of Americans through trials in England with no recourse. At the heart of such matters of sovereignty remained the core assumption of the Devine Rights, and that capitol punishment was still officially sanctioned by the Church of England.