The day after Thanksgiving doesn't make sense, because you would have TWO possibilities, Zachary Taylor (Nov. 23) and Franklin Pierce (Nov. 24). Yes, I had to look it up and check it against a perpetual calendar.
The question is not phrased as though there is a choice, so it must be something else.
The post office question must be Calvin Coolidge, since he was born on July 4th, and the post office will be closed that day whatever day of the week it falls on.
I really don't think the question implies it's a Friday of every year. It just says "...it's Friday and the post office is closed."