A weird thing is that these intermix contemporary civil timekeeping issues with historical and religious calendar issues. If you're writing software or making statements about present-day civil time, you presumably don't feel contradicted by the idea that there are also other calendars in which your assumptions don't hold. Perhaps your software and statements won't apply when people want to use those other calendars. For example, it's easy to accept that GNU date doesn't claim to state the Jewish or Islamic month or year, nor the Japanese imperial regnal year, nor the Julian date that some Eastern Orthodox Christians continue to use for some religious purposes, nor the Roman year ab urbe condita.
Your calendrical fallacy is ... not just using unix timestamps.