Under the laws given to Moses by God for the theocracy of ancient Israel, MANY things (depending on the certain factors) were capitol crimes.
However, followers of Jesus in Christian societies—while we recognize the moral laws of the Torah (Love for God, and love for neighbor—summarized in the 10 Commandments) have NEVER made the laws of ancient Israel synonymous to the laws in our societies.
As far as I know, for slightly different reasons, since before the time of Christ anyway, neither have any Jewish groups as well.
Below find a list on what the Law of God to Moses—intended for ancient Israel—found to be death-penalty offenses:
Religious practices
* Sacrificing to gods other than God alone[1][2]
* Passing children through the fire to/as [MLK]. The triconsonantal root MLK has traditionally been translated as if it were the name of an otherwise unattested deity - Molech - but may just describe a type of sacrifice. It is generally thought that this refers to a form of Human sacrifice similar to that of which the Phoenicians (particularly in Carthage) have historically been widely accused[3]
* worshipping Baal Peor[4]
* False prophecy[5][6][7]
* Necromancy, according to the masoretic text; specifically those who are masters over ghosts (Hebrew: Ba’al ob) and those who gain information from the dead (Hebrew: Yidde’oni)[8]. The Septuagint instead condemns gastromancy (Greek: eggastrimuthos), and enchantment (Greek: epaoidos)[9].
* According to the masoretic text, practitioners of kashaph[10] - incanting maleficium. According to the Septuagint version of the same passages, pharmakeia[11] - poisoners. Historically this passage has been translated into english using vague terminology, condemning witchcraft in general[12].
* Blasphemy[13]
* Sabbath breaking[14][15][16]
Sexual practices
* Rape by a man of a betrothed woman in the countryside[17]
* Being either participant in urban sexual activity, in which a betrothed woman consensually loses her virginity to a man[18]
* Loss of virginity by a woman prior to marriage, to someone other than her husband[19]
* Adultery with a married woman[20]. Sexual activity between a married man and an unmarried woman was not forbidden[21].
* Marrying your wife’s mother[22]
* Certain forms of Incest, namely if it involves the father’s wife or a daughter-in-law[23]. Other forms of incest receive lesser punishment; sexual activity with a sister/step-sister is given excommunication for a punishment[24]; if it involves a brother’s wife or an uncle’s wife it is just cursed[25]; and sexual activity with an aunt that is a blood relation is merely criticised[26].
* Prostitution by the daughter of a priest[27]
* Male homosexual activity[32][33]
* Bestiality[34][35]
Miscellaneous
* Murder, applies to Noachides as well[36][37][38][39]
* Striking a parent[40]
* Cursing a parent[41][42]
* The “degenerate son”[43]
* Kidnapping[44][45]
* Negligent homicide, specifically by ox-goring[46]
* Contempt of court[47]
* False witness to a capital crime[48]
Even back to colonial days in America sodomy was not an absolute death-penalty offense. As a Christian, naturally I do accept that such activity is a sin—and socially not desireable—but a today should it be a capitol offense? No...sorry, as America (and every other country too) is not the theocracy of ancient Israel—for whom, 3500 years ago Moses wrote down the laws from God.
If you think we should make sodomy a death penalty crime again, would you make all the items above capitol offenses too? They were also capitol crimes in the Law of God given to Moses.
I am unsure as to whether Noachide courts (which unfortunately do not exist) have the authority to execute the death penalty when there is no Beit HaMiqdash or Sanhedrion in Jerusalem. But capital offenses are still capital offenses, whether or not man is currently permitted to carry out the sentences.
There was a time when Jewish authorities, with the permission of the host government, were permitted to execute the death penalty on those Jews who (G-d forbid!) merited it. Unfortunately Jewish sovereignty in the Galut no longer exists. Needless to say, I personally would like to see it restored, with the authentic Rabbinate and Battei Din having civil authority over all Jews.
And once again, in Jewish/Noachide courts neither confessions nor circumstantial evidence are admissible. Only eyewitnesses (two in Jewish courts, one in Noachide courts) are admissible.
G-d is G-d. Most of the evils of recent millenia have been due to man trying to remake G-d in his own warped image.