David Costello and Rivkah Weber look every bit a young Orthodox Jewish couple.

Costello sports a yarmulke and sidelocks and Weber dresses modestly and covers her head.

They keep kosher and never miss Sabbath at the synagogue.

But they do share one little oddity: They believe Jesus is the Messiah.

And they are not shy about spreading their gospel, according to angry members of the Jewish community who say the couple are really Christian infiltrators fishing for converts.

Their presence has rocked synagogues in Brooklyn, and earlier this month in Chicago, after a visitor from New York recognized Costello from a Williamsburg shul and “outed” him.

“People feel betrayed,” one Illinois rabbi told the Jewish Telegraphic Agency. “If you want to believe in something and sell it, that’s your business. But to come into a community and portray to be something you’re not, prey on people, unsuspecting, is unacceptable.”

Rabbi Levi Notik, the spiritual leader at the FREE center in Chicago, which is part of the Chabad-Lubavitch movement and where the couple worshipped, alerted a Jewish newspaper about the couple this month. He refused to talk to the Post.

Another notice went out on Facebook to the Chicago Jewish community saying “Everybody is advised not to talk to them… Please do not be a hero or know-it-all, even if you may have met them and think they’re nice.”

Weber — who was born Rebekah and raised Christian — told The Post that the couple is not out to trick anyone.

“We believe in Yeshua as the Messiah,” she said using the Hebrew word for Jesus. “People don’t like that.”

To spread the word, she once put literature discussing Jesus in gift baskets she gave to Jewish families for the Purim holiday — to a decidedly mixed reaction.

She admits she wants Jews to believe in Jesus, too, but insists the couple are not missionaries or Jews for Jesus, an organization that encourages Jews to embrace Jesus as the Messiah but, Weber said, discourages traditional observance of the Torah.

Weber, 29, said the couple live an Orthodox Jewish “lifestyle.” She said she wants to convert to Judaism and that her husband was raised as a Christian but learned later that he had Jewish relatives on his mother’s side so considers himself Jewish.

While living in Brooklyn they worked for Global Gates, an evangelical Christian organization that wants “gospel transformation of the world’s most unevangelized people” including New York’s Hasidic sects.

Weber said they were with Global Gates for less than a year.

She said her husband, 37, would bring up his beliefs in discussions at Brooklyn shuls and was generally met with a frosty reception and sometimes threats of violence.

“Anytime he was asked to leave a shul, he did,” she said.

She said they left Brooklyn, where they lived in Flatbush, because it was too expensive.

Weber said since the warnings went out about them this month her husband lost his job at a kosher supermarket and they have been threatened with violence.

In a now-deleted fire-and-brimstone post on Facebook, Weber wrote to their accusers: “You all have brought shame to Judaism for how you have slandered us and even encourage others to harm us and our children. If you truly followed Torah … you would love us as the Torah commands and seek to find the truth instead of believe the lies you read.”