Although ISO date strings can be fairly trivial to read and manipulate with RexExp or a custom parser, depending on the complexity of the task, I would recommend using something like iso-fns.
It's too bad this library (and approach) never took off, but it's there to use nevertheless.
Even without iso-fns, it's not as if mid level developer can't figure out how to write a function to perform a specific operation on an ISO date string.
After over 10 years of web development, I do think this is the best known approach and is even better than storing UNIX time. Even if there were no existing libraries to help with manipulating ISO strings, I will gladly take the inconvenience in exchange for the rest of the advantages.
With ISO strings, you don't get any behavioral quirks from Date; they are totally compatible with JSON; you can store the time zone along with the time; there is nothing to stop you from changing the time zone while leaving all the other values intact; ISO strings also support durations.
Basically, they support most of what a software developer will be expected to do with times and dates but without any behavior or assumptions about the client time zone that introduce bugs like with Date. `<input type="datetime-local">` also uses ISO strings out of the box, which can be really convenient, and values from `<input type="date">` can be easily appended into an actual ISO string.