Say that a Dayak that still practices head hunting (Ngayau) moves to the United States and becomes a citizen. Is this person protected by freedom of religion or are they sent to jail when they kill someone as you are not allowed to do that?
Reynolds v. United States 98 U.S. 145 held that "A party's religious belief cannot be accepted as a justification for his committing an overt act, made criminal by the law of the land". Employment v. Smith 494 US 872 applies this to criminal acts, holding that "The Free Exercise Clause permits the State to prohibit sacramental peyote use" and "the [Free Exercise] Clause does not relieve an individual of the obligation to comply with a law that incidentally forbids (or requires) the performance of an act that his religious belief requires (or forbids) if the law is not specifically directed to religious practice and is otherwise constitutional as applied to those who engage in the specified act for nonreligious reasons". Likewise Church of the Lukumi Babalu Aye v. City of Hialeah 508 US 520 "a law that burdens religious practice need not be justified by a compelling governmental interest if it is neutral and of general applicability" (the ordinances were not narrowly taylored, unlike murder statutes). Thus laws against murder do not become unconstitutional when one proclaims a religious basis for violating the law, since they are religiously neutral and are there for good reason.
user6726's answer addresses what the Constitution requires, but many jurisdictions in the US go further in protecting religion. After cases like Employment Division v. Smith, Congress decided that religious exercise should generally be exempt from neutral laws of general applicability. They wrote that into federal law with the Religious Freedom Restoration Act, which requires that:
(a) Government shall not substantially burden a person’s exercise of religion even if the burden results from a rule of general applicability, except as provided in subsection (b).
(b) Government may substantially burden a person’s exercise of religion only if it demonstrates that application of the burden to the person—
(1) is in furtherance of a compelling governmental interest; and
(2) is the least restrictive means of furthering that compelling governmental interest.
This law only applies to the federal government; Congress can clarify that it doesn't intend to burden religion even though the Supreme Court says it's allowed to, but it can't restrict the states like that. However, a number of states have similar laws at the state level.
The test set out in the RFRA is called strict scrutiny, and it's the normal test used for laws that restrict a fundamental right or discriminate on the grounds of a suspect classification (like race). It gives a lot more protection than the rule that laws have to be religiously neutral, which is why you have cases like Hobby Lobby (in which a federal law requiring employers to pay for contraception, though religiously neutral and of general applicability, was ruled to not apply to companies with religious objections to contraception). But while it's a high bar for a law to meet, it's not insurmountable. The government has a compelling interest in protecting its citizens from being killed, and criminalizing murder is the least restrictive way to achieve that. Assault laws also easily past the test, as do laws against kidnapping, robbery, rape, theft, fraud, tax evasion, etc.