2:10 PM PT -- Fred, Esq, a rep for STX -- who also happens to be a puppet -- tells us, "STX loved the idea of working closely with Brian Henson and the Jim Henson Company to tell the untold story of the active lives of Henson puppets when they’re not performing in front of children."

Fred continues, "Happytime Murders is the happy result of that collaboration and we’re incredibly pleased with the early reaction to the film and how well the trailer has been received by its intended audience. While we’re disappointed that Sesame Street does not share in the fun, we are confident in our legal position. We look forward to introducing adult moviegoers to our adorably unapologetic characters this summer.”

This lawsuit is brought to you by the letter F because the creators of "Sesame Street" are downright Furious with producers for "The Happytime Murders" ... alleging it's taking a crap all over its good name.

Sesame Workshop is suing STX Productions -- the company behind Melissa McCarthy's new movie -- claiming its marketing strategy confuses fans into mistakenly believing Sesame is in cahoots with the movie while ruining its wholesome image.

In docs, obtained by TMZ, Sesame says its beef is with the marketing campaign that features the tagline "NO SESAME. ALL STREET" and a trailer with "explicit, profane, drug-using, misogynistic, violent, copulating and even ejaculating puppets."

What's more ... Sesame says STX does not own, control or have the right to use "Sesame Street." Sesame says it's tried to get STX to drop the act but to no avail.

So it's suing to get STX to drop the tagline and unspecified damages. We've reached out to STX ... so far no word back.