According to Judaism, non-Jews are expected to follow the Seven Laws of Noah (often called the Noahide Laws).
Jewish tradition teaches that these are ancient, universal moral commandments given by God to Noah and his family after the flood, making them binding for all of humanity.
Here is the list of the seven laws:
1) Do not worship idols: Believe in the one true God and do not pray to statues or false deities. (When I'm in a belief phase, I am a Catholic. I do not PRAY to statues, but I DO talk to them. And even as an atheist I talk to my statue of the Blessed Virgin Mother.)
2) Do not blaspheme: Do not curse God or use His name profanely. (I am working on that because a few of my friends absolutely wince when I say God Damn It.)
3) Do not commit murder: Respect the value of human life. (And any rabbi will tell you: The most important thing to know about Jewish law is that a fetus is not considered a full legal person until the moment of birth. Because of this, Jewish law actually mandates abortion if the pregnancy poses a threat to your physical or mental life. The life of the person carrying the pregnancy always takes absolute priority. So abortion is not murder.)
4) Do not commit sexual immorality: Practice moral sexual behavior, which traditionally prohibits acts like adultery and incest. (I would say that it's not adultery if everybody involved consents to such things as polyamory or even swinging, only when it's secret and sly.)
5) Do not steal: Do not take what belongs to others, whether through theft, fraud, or kidnapping. (This one really needs no commentary!)
6) Do not eat meat torn from a living animal: Practice humanity toward animals, which means not causing them unnecessary cruelty or eating flesh taken from an animal while it is still alive. (I like this one, because it teaches to be kind with creatures.)
7) Establish courts of justice: Set up a fair legal system and government to enforce these laws and ensure a just society. (Wish this one worked these days, but holy COW are SCOTUS and other courts a disaster. They've all been packed by the Orange Atrocity and are destroying the Constitution.)
In my opinion these are the most sensible rules I've ever heard, though I'm not sure about the God stuff, since I'm in a non-believing phase in my life. However, I am starting to lean back toward Catholicism.
I make this promise now:
If I DO end up in a belief phase again (my faith flows and ebbs, and I just ride with it) I swear, will not shove Jesus down your throats. I will occasionally mention things like if I ever get confirmed or if I make a rosary or have a profound thought. But I won't do daily religion.
A Catholic who follows Jewish Law for Gentiles. Interesting. And reasonable. There is room for both.