These guys don’t agree on anything — but a Republican city councilman from Staten island and his Democratic counterpart from Queens both say the NYPD should be ashamed for giving wealthy pedophile Jeffrey ­Epstein a slide on his sex-offender check-ins.

Often-at-odds Councilmen Joseph Borelli (R-SI) and Donovan Richards (D–Queens) set aside their differences Thursday to send a scathing letter to the NYPD, following a Post Page 1 story revealing that cops let Epstein ignore a court order to report to the department every three months.

“As you are undoubtedly aware, there is a popular perception that our criminal-justice system favors the wealthy. If true, this case would confirm our worst fears and strike directly at one of the fundamental tenets of our nation; justice for all,” the pols wrote to NYPD Internal Affairs Bureau Deputy Commissioner Joseph Reznick and Legal Bureau Deputy Commissioner Ernest Hart.

“How did the NYPD justify granting permission for Jeffrey Epstein to ignore a court mandated requirement based on an argument which was rejected by the highest judicial authority in the state of New York?”

The Post reported that the NYPD never once made Epstein, 66, a Level 3 perv, report to its Sex Offender Monitoring Unit — despite a state judge in 2011 ­instructing him to do just that.

His lawyers argued in court that year that he shouldn’t report to the NYPD, because he claims his primary residence is in the US Virgin Islands, but state Supreme Court Justice Ruth Pickholz said that didn’t matter and ordered Epstein — who maintains a $77 million Upper East Side townhouse at 9 E. 71st St. — to check in with the cops “every 90 days.”

But the department gave him a pass for eight years, and when confronted claimed Epstein’s island residence precluded him from scrutiny in the Big Apple — despite what the judge ruled.

Council Speaker Corey Johnson and Mayor de Blasio also questioned the NYPD’s handling of Epstein. “Something’s very broken. It’s ridiculous. He should have had to report in all the time; he’s a danger to society,” de Blasio said on MSNBC Thursday, adding he has ordered cops “to look at the situation.”

Epstein’s lawyers, meanwhile, said in Manhattan federal court Thursday that he’s willing to put up the $77 million townhouse and a private jet as collateral so he can cool his heels on house arrest with an ankle monitor while he awaits trial. His bail application will get a hearing Monday.