Red herrings do serve a purpose: they (ostensibly) make it harder for the reader to identify the true culprit. They don't inherently violate Chekhov's gun, but you do need to, at some point, bring them up again in order to explain that they're red herrings.
For example, let's say you have a detective investigating a death by shooting, and they find three different guns that implicate three different suspects and could all have been used in the shooting. Two of those guns are red herrings, and the detective's summation needs to explain how they know that Gun A was used and not Guns B and C.
One of my favourite examples of a red herring is the What's New, Scooby-Doo? episode "Roller Ghoster", where an amusement park is being terrorised by a monster. There's an extremely obvious red herring in the form of a kid who keeps getting turned away from rides for being too short, and gets increasingly furious about it. At the end of the episode, after the monster has been caught and unmasked, the kid shows up and asks, "How come I wasn't a suspect?", to which Velma bluntly replies, "You're too short to fit in the costume". Had he not made that appearance at the end, it would have been a violation of Chekhov's gun.
(Before anyone brings him up, I know A Pup Named Scooby-Doo has a character literally called "Red Herring", but in most episodes he doesn't actually appear until Fred randomly accuses him at the end, so he's not relevant to OP's problem.)