The trigger warning “puppet nudity” does not begin to cover it. You will also see puppets having sex, singing about being “a little bit racist” and gleefully owning up to their predilections for porn.

Avenue Q’s cute subversiveness is back, 20 years after these fuzzy-felt Sesame Street wannabes took the West End by storm. Robert Lopez and Jeff Marx’s Tony award-winning musical is not exactly shocking now but it’s very amusing as these creatures (plus some humans) fall in love, have existential crises and create merry havoc.

Directed by Jason Moore on Anna Louizos’s house-lined set, as flat as a child’s drawing, it kicks off with the arrival of bushy-tailed college graduate Princeton (Noah Harrison) on the titular New York street, and leads into his romance with Kate Monster (a Shrek-like outsider played by Emily Benjamin) and his search for life’s greater meaning. His new neighbours include plain-speaking Japanese therapist Christmas Eve (Amelia Kinu Muus), former child star turned handyman Gary (Dionne Ward-Anderson), and Rod (also Harrison) and Nicky (Charlie McCullagh) – flatmates in the mould of Sesame Street’s Bert and Ernie.

There is a noughties naughtiness to songs like If You Were Gay, Everyone’s a Little Bit Racist and The Internet Is for Porn, the last led by Trekkie Monster exuding Cookie Monster-turns-dirty vibes. These songs go all-out to bust taboos and might have sounded explosive back in the day. The subject matter is still current (from the resurgence of homophobia to the revival of Black Lives Matter), but not as charged in shock value. The hammy Japanese accent by Austrian-Japanese performer Kinu Muus is possibly the most striking thing. There is also the pre-#MeToo moniker of Lucy (“the slut”), an influencer who looks like a puppet version of Bonnie Blue with a plunging neck-line (“yeah, they’re real”, she coos).

The force of the show’s faux-naivety works because of the comic dissonance between the puppets’ innocence – wide eyes, cutesy voices – and their adult misbehaviour (drunkenness, pole dancing, sex and betrayal). Lopez and Marx’s songs are a blast, from the cleverness of Schadenfreude to the melancholy in Kate’s break-up song, There’s a Fine, Fine Line, and the closeted hilarity of Rod singing My Girlfriend, Who Lives in Canada. Every number is performed with such physical and vocal exuberance by the cast of actor-puppeteers, especially the spectacular Harrison and Benjamin, that it really does seem as if the puppets are doing the talking, singing and shagging.

Puppet designer Rick Lyon’s furry creations are winkingly derivative (he worked on Sesame Street for 15 seasons). It is a recognisably clever riff on the children’s show, with its animation breakouts, preschool educational lessons and Oscar the Grouch’s signature dustbins in the backdrop. But the kooky satire also stands on its own terms. Jeff Whitty’s award-winning book has been updated with jokey mentions of AI, OnlyFans and Spotify, while the song Mix Tape has a tongue-in-cheek reference to such an “olden days” phenomenon.

The production trades off its sweet/subversive/manic charms and the story itself is not especially strong. But who cares? It brings such sunny puppet-bound escapism while never quite leaving our world and the mess that human beings have created in it. The show ends on a hopeful note with heavy helpings of “this too will pass” spirit. It is all only for now, the puppets tell us – even Trump.

• At Shaftesbury theatre, London, until 29 August