Chillul HaShem:Failure to punish that which is viewed as sinful by non-Jews/ Rosh

Rosh(17:8): [Translation Prof. Aaron Schreiber] Question: Let it be known to our teacher, may he be well, that here in Cordova a very serious incident took place. The ears of all those who hear of it become “singed.” A certain debased person was detained on charges by Gentiles. He settled with them by paying money. Some of his acquaintances later went to console him. He went out [to welcome them] and stood at the.’ Entrance of his yard. They calmed him in this matter, one of them saying, “Blessed is he who frees the imprisoned.” Nevertheless, he, turning upward, [to heaven], blasphemed and reviled his King and God . . .. About ten of the community notables, men of action, with  this honorable [man] Rabbi Judah, and local sages, with the city elders [decided] to do away with him. Learning of this, relatives of the guilty person went with bribes, it seems, to the great royal dignitary, Don Juan Manuel whom we received in our area as the procurator for his majesty, the king . . ..  This lord agreed that the guilty one should remain in his prison until the Responsum of my teacher will arrive instructing [us] what to do . . .. Response: May the delightful pious and charming notables accept [the blessing of] abundant peace! Your asking me concerning capital cases is rather strange. In all of the lands that I have heard of they do not try capital cases except in this land of Spain. When I came  here I was very astonished. How were they able to try capital cases without the Sanhedrin? They replied that it is by royal authority. The assembly [of judges] also judges in order to save [lives], since greater amounts of blood would have been spilled if they were tried by the gentiles. I permitted them to continue with their practice. However, I never agreed with them on any loss of life. Nevertheless, I see that all of you are of the opinion to remove this evil from your midst. He certainly did desecrate the name of heaven in public and it was already heard by the Gentiles, who view with seriousness anyone who speaks against their  religion and beliefs. The desecration would be increased if no act of vengeance would be taken against him. We do find that in order to sanctify the name of God they raised their hands against princes on behalf of proselytes [see 2 Sam. 21: 8-9] and let their [the princes’] corpses hang overnight. [We also find] that in order to check lawlessness they stoned to death a person who had ridden a horse on the Sabbath [see Talmud, Yebamot 90b]. It is also proper that God’s name should be sanctified by the loss of this wicked person, and so as you see fit. If I were present at your contemplations, my opinion would be to cut off the major portion of his tongue necessary for speech thereby silencing his lips. In  his way they would mete out [punishment] to him according to his deed. This is a well known vengeance which is witnessed daily. You, however, do according to what seems proper in your eyes. I do realize that your intentions are that God’s name should be sanctified.