“Doing otherwise is behavior up with which we should not put.”
Variations of that have often been used to denigrate proper grammar, implying that proper grammar is too stilted to deserve adherence.
The original statement is usually attributed to Winston Churchill, and has been quoted by many institutions in the past, including the grammar manual of the Harvard English Department.
The authenticity of attribution is still debated. Regardless, I dispute the use of such sentences to vilify proper grammar.
The mistake made by many (supposed) academic experts - including (ostensibly) Churchill - lies in conflating a specific word with a part of speech.
A preposition is a part of speech, not a word. It is true that several words are only known to function as prepositions in proper usage, but relying on that is deceptive.
I argue that in the above statement posted by you - and in the variations used in grammar manuals - the word “up” is functioning not as a preposition, but as an adverb modifying the verb “put”:
Put where? Put up!
“With” is indeed functioning as a preposition in your posted sentence, and belongs adjacent to “which”; while still formal, the resulting version is not stilted:
“Doing otherwise is behavior with which we should not put up.”
I repeat: A specific word is not the same thing as a part of speech.
I hope Santa brings you a sense of humor for Christmas.