Forecast Palindromic Dates
MATL, 24 23 bytes
YOZ}&amp;:&quot;@23XOtt47&gt;)tP=?8M

Accepts  input in the form of an array of string {lower, upper} where the date format is 'MM/DD/YYYY'. Output is in the format MM/DD/YYYY as well.
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Explanation
        % Implicitly grab the two inputs
YO      % Convert to serial date format
Z}      % Push them onto the stack separately
&amp;:      % Create an array from [lower...upper] incrementing 1 day
&quot;       % For each day
  @23XO % Get the string version of the date (mm/dd/yyyy)
  tt    % Duplicate twice
  47&gt;)  % Get the numeric parts
  tP=   % Compare numeric part with the flipped version of the numeric part
  ?8M   % If they are the same push it to the stack
        % Implicitly display stack contents