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This timestamp is the "0" epoch timestamp (in PST). Somewhere along the lines, either in Tableau or in the DB, your data is getting typecasted and it is converting it to that datetime.
If you can't track it down to something you can control (in the DB for example), then you can do something like this, which will null it out again:
IF [myDate] <> #12/31/1969# THEN [myDate] END
Thanks for your response, Derrick! I took your advice and tweaked it slightly. Thanks for helping me get on the right path! Here's how it ended up:
IF [myDate] < #1/1/1970# THEN NULL