With me, it is more a question of "can't watch" rather than "can't stand". There are several movies, recommended by people whose taste I trust, that I cannot just get into after two or three attempts, such as:
Welcome to the Dollhouse (1995) dir: Todd Solondz
Under the Skin (2014) dir: Jonathan Glazer
Trainspotting (1996) dir: Danny Boyle
The Lion in Winter (1968) dir: Anthony Harvey
Short Cuts (1993) dir: Robert Altman
Requiem for a Dream (Dir Cut) (2000) dir: Darren Aronofsky
Heathers (1998) dir: Michael Lehmann
Call Me by Your Name (2017) dir: Luca Guadagnino
Blue Valentine (2010) dir: Derek Cianfrance
Not sure how many of the above you consider "classics" but they are all acclaimed and serious movies I would be expected to like. In many cases I have enjoyed other films by the same directors. There are plenty more that I cannot call to mind just now. They are a varied batch, but in each case I have not got the patience to watch them, and reach for the "eject" button on my control.
Things can change with time. I was very disappointed with
Night Moves (1975) dir: Arthur Penn. I liked it more on second viewing, and watched it a third time the other night and thoroughly enjoyed it. That's a different situation though. I was able to watch all through first time, just felt "cheated' thereafter (because I had the wrong expectations), whereas the above titles just irritate me to watch for various reasons and I have never got past halfway at best.