Films I really enjoy and have watched many times, but they are (cough) problematic.
Pretty Woman - love it but it does majorly trivialise prostitution and supports men buying women
The Parent Trap - WTAF. Parents split and take one twin each and don't tell them or ever meet up?
Breakfast at Tiffany's - it's not a comedy! Holly was a sexually exploited child bride.
Gone with the Wind - dear lord, the cover up of slavery is awful.
I'm sure there are others ...