User space doesn't generally deal well with time going backwards, but the main problem is that setting an absolute timeout in a program is broken when the target time is less than the current time. An example of this is 32-bit systemd, which just hangs at boot when the RTC points to a time after 2038, as it tries to figure out of timers work.

https://www.adelielinux.org/ is an example of a Linux distro built on musl-1.2, so you can use that beyond 2038 on 32-bit hardware.