Think hard about whether your use case really cares about local time, try and find ways to make instants appropriate. Then stick to UTC ISO 8601 strings / Unix timestamps and most of the complexity goes away, or at least gets contained to a small part of your software.
I know this isn't always possible (I once had to support a feature that required the user took a break covering two periods of 1-5am local, which was obviously fun around DST boundaries) - but in my experience at least the majority of the time you can find ways to minimise the surface area that cares.
If you're passing raw/unvalidated user input to the date parser you're holding it wrong.